Foundations of Energy Harvesting and Energy Cooperating Wireless - - PowerPoint PPT Presentation

Aylin Yener Penn State (on leave at Stanford) yener@{engr.psu, stanford}.edu

WiOpt 2017 GREENNET Keynote May 19, 2017

Foundations of Energy Harvesting and Energy Cooperating Wireless Communications

Introduction

Ubiquitous Mobile / Remote

Energy-limited

5/19/17

Many sources Abundant energy

Green

Energy Harvesting

Wireless Communications Energy Harvesting Wireless Networks

GREENNET

Energy Harvesting Networks

§ Wireless networking with rechargeable (energy harvesting) nodes: § Green, self-sufficient nodes, § Extended network lifetime, § Smaller nodes with smaller batteries.

5/19/17 GREENNET

What could EH bring to communications?

5/19/17 GREENNET

Wireless Energy Cooperation

5/19/17 GREENNET

5/19/17 GREENNET

Personal access point Motion sensor Heart sensor Wearable

Energy Harvesting Applications

Body area networks

Energy Harvesting Applications

MC10’s biostamps for medical monitoring, powered wirelessly

Image Credits: (top) http://pubs.acs.org/doi/abs/10.1021/nl403860k#aff1 (bottom) ) http://www.dailymail.co.uk/ sciencetech/article-2333203/Moto-X-Motorola-reveals-plans-ink-pills-replace-ALL-passwords.html

KAIST’s Solar charged textile battery

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Energy Harvesting Applications

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) https://assist.ncsu.edu/research/

Health tracker utilizing solar cells

5/19/17 GREENNET

In-body (intravascular) wireless devices

Image Credits: (top) http://www.extremetech.com/extreme/119477-stanford-creates-wireless-implantable-innerspace-medical-device (middle) http://www.imedicalapps.com/2012/03/robotic-medical-devices-controlled-wireless-technology-nanotechnology/ (bottom) http://scitechdaily.com/smart-pills-will-track-patients-from-the-inside-out/

Energy Harvesting Applications

Proteus Biomedical pills, powered by stomach acids

5/19/17 GREENNET

What is in it for us?

§ New: communication theory of EH nodes § New: information theory of EH nodes Key new ingredient: A set of energy feasibility constraints based

• n harvests govern the communication

resources.

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Communications

§ New Wireless Network Design Challenge: A set of energy feasibility constraints based

• n harvests govern the communication

resources. § Design question: When and at what rate/power should a “rechargeable” (energy harvesting) node transmit? § Optimality? Throughput; Delivery Delay § Outcome: Optimal Transmission Schedules

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Two main metrics

§ Short-Term Throughput Maximization (STTM): Given a deadline, maximize the number of bits sent before the end of transmission. § Transmission Completion Time Minimization (TCTM): Given a number of bits to send, minimize the time at which all bits have departed the transmitter.

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§ 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 è BATTERY CAPACITY.

ST Throughput Maximization

[Tutuncuoglu-Y. 2012]

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§ Energy harvesting transmitter: § Transmitter has data to send by deadline T § Energy arrives intermittently from harvester § Stored in a finite battery of capacity

System Model

Ei

transmitter receiver

Energy queue Data queue

Emax Emax

5/19/17 GREENNET

§ Energy arrivals of energy at times § Arrivals known non-causally by transmitter, § Design parameter: power rate .

i

E

i

s

) ( p r

→

E0

t

T E1 E2 E3 s1 s2 s3 s0

System Model

5/19/17 GREENNET

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 p
• iii. strictly concave
• iv. r(p) continuously differentiable

Example: AWGN Channel,

) (p r

Rate Power

⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + = N p p r 1 log 2 1 ) (

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Notations and Assumptions

§ Power allocation function: § Energy consumed: § Short-term throughput: ∫

T

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

∫

T

dt t p ) (

Concave rate in power àGiven a fixed energy, a longer transmission with lower power departs more bits.

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§ Battery Capacity:

Energy Constraints

(Energy arrivals of Ei at times si) § Energy Causality:

n n n i t i

s t s dt t p E ≤ ≤ ≥ −

− − =

∑ ∫

' ) (

1 1 ' n n n i t i

s t s E dt t p E ≤ ≤ ≤ −

− − =

∑ ∫

' ) (

1 1 ' max

⎭ ⎬ ⎫ ⎩ ⎨ ⎧ ≤ ≤ > ∀ ≤ − ≤ =

− − =

∑ ∫

n n n i t i

s t s n E dt t p E t p ' ) ( ) (

1 1 ' max

, ,

§ Set of energy-feasible power allocations

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Energy “Tunnel”

c

E

t

1

s

2

s

E

1

E

2

E

max

E

Energy Causality Battery Capacity Feasible Policy

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Optimization Problem

§ Maximize total number of transmitted bits by deadline T § Convex constraint set, concave maximization problem

∫

∈

T t p

t p t s dt t p r

) (

) ( . . , )) ( ( max

⎭ ⎬ ⎫ ⎩ ⎨ ⎧ ≤ ≤ > ∀ ≤ − ≤ =

− − =

∑ ∫

n n n i t i

s t s n E dt t p E t p ' ) ( ) (

1 1 ' max

, ,

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Necessary conditions for

• ptimality of a transmission policy

§ Property 1: Transmission power remains constant between energy arrivals. § Let the total consumed energy in epoch be which is available at .Then the power policy is feasible and better than a variable power transmission; shown easily using concavity of r(p)

5/19/17

] , [

1 + i i s

s

total

E

i

s t =

] , [ ,

1 1 + +

∈ − = ′

i i i i total

s s t s s E p

GREENNET

§ Property 2: Battery never overflows. Proof:

p r(p) dt r(p(t)) dt (t)) p r( else t p t p t p

T T

in increasing is since Then Define time at

• verflows
• f

energy an Assume

∫ ∫

> ′ ⎪ ⎭ ⎪ ⎬ ⎫ ⎪ ⎩ ⎪ ⎨ ⎧ − Δ + = ′ Δ ) ( ] , [ ) ( ) ( τ δ τ δ τ

Necessary conditions for optimality

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Necessary conditions for

• ptimality of a transmission policy

§ Property 3: Power level increases at an energy arrival instant

• nly 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))dt p r(

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Necessary conditions for

• ptimality of a transmission policy

§ Property 3: Power level increases at an energy arrival instant

• nly 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))dt p r(

p*(t)

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Necessary conditions for

• ptimality of a transmission policy

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

increasing is since Then Define p(t) after remains

• f

energy an Assume r(p) dt r(p(t)) dt (t)) p r( else t p T T t p t p

T T

∫ ∫

> ′ ⎪ ⎭ ⎪ ⎬ ⎫ ⎪ ⎩ ⎪ ⎨ ⎧ − Δ + = ′ Δ ) ( ] , [ ) ( ) ( δ δ

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Implications of the properties

[Tutuncuoglu-Y. 2012]

§ Structure of optimal policy is piece-wise linear. § For power to increase or decrease, policy must meet the upper or lower boundary of the tunnel respectively. § At termination step, battery is depleted. § Utilizing this structure, a recursive algorithm emerges to find the unique optimum policy [Tutuncuoglu-Y. 2012]. constant , } { , ) (

1 n n n n n n

p s i T t i t i p t p ∈ ⎭ ⎬ ⎫ ⎩ ⎨ ⎧ > < < =

−

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Energy “Tunnel”

c

E

t

1

s

2

s

E

1

E

2

E

max

E

Energy Causality Battery Capacity Feasible Policy

5/19/17 GREENNET

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 +

− = p p r

∈ + =

∫

) ( . . 1 ) ( min

2 ) (

t p t s dt t p

T t p

length of policy path in energy tunnel

∈ + −

∫

) ( . . 1 ) ( max

2 ) (

t p t s dt t p

T t p

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Shortest Path Interpretation

§ Property 1: Constant power is better than any other alternative § Shortest path between two points is a line (constant slope)

E

t

5/19/17 GREENNET

Alternative Solution (Using Property 1)

§ Transmission power is constant within each epoch: § KKT conditions à optimum power policy.

N n E p L E t s p r L

n i i i i N i i i pi

,..., 1 . . ) ( . max

max 1 1

= ≤ − ≤ ∑

∑

= =

} 1 , { ) ( ,N , i i epoch t , p t p

i

… = ∈ =

(Li: length of epoch i) (N: Number of arrivals within [0,T])

5/19/17 GREENNET

1 max 1

= ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − − = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ −

∑ ∑

= = n i i i i n n i i i i n

E p L E E p L full is battery when

• nly

positive

• nly

's empty is battery when

• nly

positive are 's µ λ

Solution

§ Complementary Slackness Conditions:

n E p L E n E p L

n i i i i n n i i i i n

∀ = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − − ∀ = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ −

∑ ∑

= = 1 max 1

µ λ

n n N n j j j n

p µ λ µ λ positive with decreases positive with increases 1 ) ( 1

* + =

⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ − − = ∑

5/19/17 GREENNET

Directional Water-Filling

§ [Ozel, Tutuncuoglu, Ulukus, Y., 2011] § Harvested energies filled into epochs individually

t O O O

E

1

E

2

E

Water levels (vi)

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Directional Water-Filling

§ Harvested energies filled into epochs individually § Constraints:

§ Energy Causality: water-flow only forward in time

t O O O

E

1

E

2

E

Water levels (vi)

5/19/17 GREENNET

Directional Water-Filling

§ Harvested energies filled into epochs individually § Constraints:

§ Energy Causality: water-flow only forward in time § Battery Capacity: water-flow limited to Emax by taps

t O O O

E

1

E

2

E

Water levels (vi)

5/19/17 GREENNET

Example

2

0 =

E 5

1 =

E

1

s p 1

2 =

E 9

3 =

E 7

4 =

E

2

s

3

s

4

s

10

max =

E

5/19/17 GREENNET

Directional Water-Filling

§ Energy tunnel and directional water-filling approaches yield the same policy

E

t t O O O

E

O O O

E

1

E

2

E

3

E

4

E

5

E

1

E

2

E

3

E

4

E

5

E

5/19/17 GREENNET

Directional Water-Filling

§ Energy tunnel and directional water-filling approaches yield the same policy

E

t t O O O O O O

5/19/17 GREENNET

Simulation Results

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

5/19/17 GREENNET

Fading Channels

[Ozel-Tutuncuoglu-Ulukus-Y.‘11]

§ AWGN Channel with fading h : § Each “epoch” defined as the interval between two “events”.

) 1 log( 2 1 ) , ( hp h p r + =

E

2

E

3

E

6

E

7

E

t x x x x Fading levels

L1 L4 L7 h1 h2=h3=h4 h5 h6=h7 h8

,.. 5 , 4 , 1

= E

O O O O O

5/19/17 GREENNET

Directional Water-Filling for Fading Channels

t O O O x

E

2

E

4

E

Fading levels (1/hi) Water levels (vi) x

§ Same directional water filling with base levels adjusted according to channel quality.

§ Directional water flow (Energy causality) § Limited water flow (Battery capacity)

5/19/17 GREENNET

§ Given the total number of bits to send as B, complete transmission in the shortest time possible.

Transmission Completion Time Minimization (TCTM)

∫

∈ ≤ −

T t p

t p dt t p r B t s T

) (

) ( , )) ( ( . . min

⎭ ⎬ ⎫ ⎩ ⎨ ⎧ ≤ ≤ > ∀ ≤ − ≤ =

− − =

∑ ∫

n n n k t k

s t s n E dt t p E t p ' , , ) ( ) (

1 1 ' max

5/19/17 GREENNET

= max

u≥0

min

T

T + uB − u.max

p(t )∈P

r(p(t))dt

T

∫

( )

⎛ ⎝ ⎞ ⎠

§ Lagrangian dual of TCTM problem becomes:

Relationship of STTM and TCTM

⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − +

∫

∈ ≥ T T P t p u

dt t p r B u T

, ) (

)) ( ( min max

STTM problem for deadline T

5/19/17 GREENNET

§ Optimal allocations are identical: § STTM solution can be used to solve the TCTM problem

STTM’s solution for deadline T departing B bits TCTM’s solution for departing B bits in time T

≡

5/19/17 GREENNET

Relationship of STTM and TCTM

Maximum Service Curve

§ Continuous, monotone increasing, invertible § Optimal allocation for TCTM with B1 bits Optimal allocation for STTM with deadline T1

1

S

2

S Deadline (T)

3

S Maximum Departure (B) s(T)

T1 B1

=

5/19/17 GREENNET

Transmission Policies with Inefficient Energy Storage

§ Energy stored in a battery, supercapacitor, . . . § “Real life” issues: § [Devillers-Gunduz ‘12]: Leakage and Degradation § [Tutuncuoglu-Y.-Ulukus ‘15]: Storage/Retriaval Losses

Storage Loss Leakage Degradation Recovery Loss

5/19/17 GREENNET

Battery Degradation

§ [Devillers-Gunduz ‘12] § Optimal Policy: Shortest path within narrowing tunnel

Degradation

E

t

5/19/17 GREENNET

Battery Leakage

§ [Devillers-Gunduz ‘12] § Optimal Policy: When total energy in an epoch is low, deplete energy earlier to reduce leakage.

E

t Leakage

5/19/17 GREENNET

Storage/Recovery Losses

§ [Tutuncuoglu-Y.-Ulukus ’15] § Main Tension:

Storage Loss Recovery Loss Concavity of r(p): Use battery to maintain a constant power transmission Battery inefficiency: Storing energy in battery causes energy loss

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§ Time slots of duration § Energy harvests: Size Ei at the beginning of time slot i

Time slotted model

E1

t

E2 E3 EN-1

τ τ 2 τ ) 1 ( − N 1 = i 2 = i . . . N i = τ N . . .

s 1 = τ

5/19/17 GREENNET

hi

Transmitter Receiver

Energy storage (ESD)

Emax si η ui pi = hi – si + ui

System Model

Rate: r(p(t))

§ hi: Harvested power § si: Stored power § ui: Retrieved (used) power § pi: Transmit power

§ ESD has finite capacity Emax and storage efficiency η. § Energy Causality: § Storage Capacity:

N i , u s

i n n n

,..., 1

1

= ≥ −

∑

=

η

N i , E u s

i n n n

,..., 1

max 1

= ≤ −

∑

=

η

5/19/17 GREENNET

§ Find optimal energy storage policy that maximizes the average throughput of an energy harvesting transmitter within a deadline of N time slots.

Throughput Maximization

{ }

. , , 1 , , , , , , 1 , ) ( . . ) ( max

max 1 1 ,

N i u s u s E N i E u s E t s u s E r

i i i i i i n i i N i i i i r s

i i

… … = ≥ ≥ ≥ + − = ≤ − + ≤ + −

∑ ∑

= =

η

5/19/17 GREENNET

Throughput Maximization

{ }

. , , 1 , , , , , , 1 , ) ( . . ) ( max

max 1 1 ,

N i u s u s E N i E u s t s u s E r

i i i i i i n i i N i i i i r s

i i

… … = ≥ ≥ ≥ + − = ≤ − ≤ + −

∑ ∑

= =

η

{ }

. , , 1 , , , , 1 , ) ( . . ) ( max

max 1 1

N i p N i E p E t s p r

i i n i i N i i pi

… … = ≥ = ≤ − ≤∑

∑

= =

Old problem:

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§ Structure of optimal policy:

[ ]

⎪ ⎩ ⎪ ⎨ ⎧ ≤ ≤ ≤ ≥ =

+ , , , , , , i u i i u i s i i u i i s i i s i

p E p p E p E p E p p

Optimal Power Policy

pi

i u

p ,

i s

p , Ei

“Double Threshold Policy”

5/19/17 GREENNET

Optimal Power Policy

* ,i u

p

* ,i s

p

* ,i u

p

* ,i s

p pi Ei

i =1

pi

*

i = 2 i = 3 i = 4 i = 5

5/19/17 GREENNET

Optimal Power Policy

(Fading channel)

pρ,i

*

* ,i s

p

* ,i u

p

* ,i s

p pi

i =1 i = 2 i = 3 i = 4 i = 5

Ei

1 hi

5/19/17 GREENNET

§ So far, we have discussed offline policies. § Energy harvesting scenario may not be predictable, or may not be available prior to transmission

Optimal Online Policy

§ Markov Decision Process (MDP) formulation:

§ Action: § Value:

) , (

i i i i

h E g p =

( ) ( ) ( ) [ ]

) , ( ), , ( max ), , ( ), , ( max ) , (

1 1 1 1 + + + + =

+ = ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ + =

∑

i i i i i i i N i n i i i i i i i i i i i

h E J h h E g r h h E g r h h E g r h E J

i i

E E

π π 5/19/17 GREENNET

Optimal Online Policy

5/19/17 GREENNET

§ Both offline and online policies point to thresholds § Choose fixed thresholds throughout transmission to satisfy

Proposed Online Policy

{ }

{ }

⎪ ⎩ ⎪ ⎨ ⎧ ≤ + ≤ ≤ ≥ − + =

u i i i u s i u i s i i i s i

p E S E p p E p E p E E S E p p , min , max

max

) ( ) ( ) ( ) ( = − − −

∫ ∫

∞

u s

p E u p E s

de e p e p de e p p e η

5/19/17 GREENNET

Simulations

0.2 0.4 0.6 0.8 1 1.4 1.45 1.5 1.55 1.6 1.65 1.7 Storage efficiency, η Throughput per Hz (Bits/s/Hz) Optimal offline policy Efficiency−adaptive DWF Directional water−filling Optimal online policy Proposed online policy

W/Hz N MHz B dB h J ] , [ ~ i.i.d. U E E mJ E ms τ s time slot N

i 19 max 4

10 1 100 200 1 10 10

−

= = − = = = = = µ

5/19/17 GREENNET

Multiple EH Transmitters

§ How to transmit when there are more than one energy harvesting transmitters sharing the same medium? § Many multi-node models, e.g.,

§ MAC and BC [Ozel-Yang-Ulukus ’11,’12], § Relay [Cui-Zhang ’12], [Oner-Erkip ’13] § Two-way Relay Ch. [Tutuncuoglu-Varan-Yener ’15], § Interference Channel [Tutuncuoglu-Yener ‘12]

1 1

a

b

E1,i

E1

max

R1 R2 T1 T2

E2,i

E2

max

5/19/17 GREENNET

Iterative Generalized Directional Water-filling (IGDWF)

4 3 9 12 8 6 2 6

v1 v2

GDWF for User 1

5/19/17 GREENNET

4 3 9 12 8 6 2 6

v1 v2

GDWF for User 2

Iterative Generalized Directional Water-filling (IGDWF)

5/19/17 GREENNET

4 3 9 12 8 6 2 6

v1 v2

GDWF for User 1

Iterative Generalized Directional Water-filling (IGDWF)

5/19/17 GREENNET

Multiple EH Transmitters: Energy Cooperation

§ Intermittent energy nodes may be energy deprived!

⇒

§ Energy cooperation between nodes can be very useful!

§ [Gurakan-Ozel-Ulukus ’12] § [Tutuncuoglu-Y. ’13]

T1 T2 R1

5/19/17 GREENNET

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

§ 50 percent efficiency at 6 feet (MIT) § 90 percent efficiency at 3 feet (MIT). § 75 percent efficiency at 2-3 feet (Intel).

5/19/17 GREENNET

Energy Harvesting and Energy Cooperation (EH-EC)

§ K transmitters receive energy Ej,i at the ith time slot § In slot i, node k transmits with power pk,i

E1,i p1,i

T1

E2,i p 2,i

T2

α2 α1 δ2,i δ1,i

§ Transmitters wirelessly transfer energy to each other

5/19/17 GREENNET

EH-EC

§ In time slot i, Tk sends to Tj, k,j =1,2, with end-to-end efficiency § Uni-directional EC is a special case with

{ }

i k i j j i k i k bat i k k bat i k

p E E E E

, , , , 1 , max ,

, min − + − + =

−

δ α δ

Harvested energy Received and sent energy Energy used for transmission

α2 α1 α2 = 0 δk,i αk

§ Battery state at time slot i:

E1,i p1,i

T1

E2,i p 2,i

T2

δ2,i δ1,i

5/19/17 GREENNET

EH-EC

Energy Constraints: § Non-negativity:

( )

1 , , , , ,

≥ − − + = ∑

= i n n k n k n j j n k bat i k

p E E δ δ α pk,n ≥ 0, δk,n ≥ 0, k =1,2, n =1,..., N

§ Energy causality: § No-Battery-Overflow:

max , k bat i k

E E ≤

5/19/17 GREENNET

§ Sum-rate:

EH-EC Two Way Channel

), , ( ~

2 2 1 1 2 2 1 2 2 1 1 k k

N N X h X Y N X h X Y σ N + + = + + =

⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + + ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + =

2 1 2 2 2 2 1 1 2 1

1 log 2 1 1 log 2 1 ) , ( σ σ p h p h p p rTWC

α2 α1 E1,i p1,i E2,i p 2,i δ2,i δ1,i

T2 T1

5/19/17 GREENNET

Problem Statement

max

pk,i, δk,i

rTWC(p1,n, p2,n)

n=1 N

∑

s.t. pk,i ≥ 0, δk,i ≥ 0, Ek,n +α jδj,n −δk,n − pk,n

( )

n=1 i

∑

≥ 0 j,k =1,2, j≠ k, i =1,..., N

§ Maximize sum-throughput by jointly optimizing the transferred energy and transmit power. § First assume infinite battery.

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Procrastinating Policies

§ Definition: A procrastinating policy satisfies i.e., the energy received by a node is not greater than the energy required for transmission in each time slot. § In a procrastinating policy, a node does not transfer energy unless the receiving node intends to use it immediately. § Theorem: (Tutuncuoglu-Y.15): There exists an optimal policy that is procrastinating.

pk,i −α jδj,i ≥ 0, k, j =1,2, k ≠ j

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Decomposition of the Sum-Throughput Problem

max

pk,i

{ }

r

S (p1,i, p2,i) i=1 N

∑

s.t. Ek,n − pk,n

( )

n=1 i

∑

≥ 0, k =1,2, i =1,..., N, pk,i ≥ 0, k =1,2, i =1,..., N.

§ Define consumed powers § Sum-throughput maximization can be decomposed as

pk,i = pk,i +δk,i −α jδj,i

r

S = max δk,i rTWC

pk,i +α jδj,i −δk,i " # $ %

( )

s.t. δk,i ≥ 0, pk,i −δk,i ≥ 0, k =1,2.

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

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EC-EH-TWC

4 3 9 12 8 6 2 6

v1 v2

E1,1 = 2 E1,2 = 5 E2,2 = 4 E2,4 = 7

α1 = 0.5 α2 = 0.5

i =1 i = 2 i = 3 i = 4

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4 3 9 12 8 6 2 6

v1 v2

δ1,1 =1 δ2,4 = 2

p1,1 = 2 p1,2 = 2 p1,3 = 2 p1,4 =1 p2,1 = 0 p2,2 = 2 p2,3 = 2 p2,4 = 7

α1 = 0.5 α2 = 0.5

E1,1 = 2 E1,2 = 5 E2,2 = 4 E2,4 = 7

i =1 i = 2 i = 3 i = 4

EC-EH-TWC

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Finite Battery Extension

[Tutuncuoglu-Y.15]

( )

,...,N i k j , k j, E p E p t s p p r

k i n n k n k n j j n k i k i k N n n n TWC p

i k i k

1 , , 2 1 , , . . ) , ( max

max , 1 , , , , , , 1 , 2 , 1 ,

, ,

= ≠ = ≤ − − + ≤ ≥ ≥

∑ ∑

= =

δ δ α δ

δ

§ Problem definition: § Postponing energy transfers may result in battery overflow § Pure procrastinating policies no longer optimal

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§ Definition: A partially procrastinating policy satisfies § Split transferred energy as

Partially Procrastinating Policies

pk,i −α jγ j,i ≥ 0, γk,iγ j,i = 0, k, j =1,2, k ≠ j ρk,i Ek

max − Sk,i

( ) = 0, k =1,2,

δk,i =γk,i + ρk,i, γk,i,ρk,i ≥ 0.

Immediately consumed comp. Stored comp.

§ Consumed comp. must immediately be used, § Stored comp. must be zero unless battery is full. § Problem solved via 2D directional water-filling with restricted transfers

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0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 1.7 1.75 1.8 1.85 1.9 1.95 2 Energy transfer efficiency from T1 to T2 (α1) Sum−throughput per Hz (bits/s/Hz) Full energy cooperation No excess energy transfers No energy cooperation One−way EC from T1 to T2

Numerical Results

N =100, T =1sec, h

1 = −100dB,

h2 = −100dB, N0 =10−19W / Hz E1,i ~ U[0,10]mJ, E2,i ~ U[0,10]mJ, α2 = 0.5

§ TWC:

Energy transfer from T1 to T2 is optimal after this point

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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 symbol level, i.e., each input symbol is individually limited by EH constraints?

Tx ¡

i

E

Rx ¡

Rate : r(p)

i

X

ENC ¡

i

E

DEC ¡ 1 1 0 0 0 1

i

Y

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[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)

ENCODER ¡

i

X W

Energy Harvesting (EH) Channel

Ei

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Binary Noiseless EH Channel

[Tutuncuoglu-Ozel-Y.-Ulukus ’13, ’14, 17’]

§ Transmitting requires units of energy § Unit battery, § Binary noiseless channel, Yi = Xi

1

max =

E

ENCODER ¡ DECODER ¡

Yi = Xi W ˆ W Emax =1 Si ∈ 0,1

{ }

Ei

Xi ∈ 0,1

{ }

Xi ∈ 0,1

{ }

Xi

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Conclusion

§ New wireless communications paradigm: energy harvesting nodes § New design insights arising from § new energy constraints § energy storage limitations and inefficiencies § interaction of multiple EH transmitters § energy cooperation § New problems in the information theory domain § Still lots of open problems related to all layers of the network design.

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Acknowledgements

§ NSF by the following grants: CNS0964364, CCF1422347, CNS1526165, § Collaborators on papers summarized in this talk are: Omur Ozel, Kaya Tutuncuoglu, Sennur Ulukus, Jing Yang.

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§ [Yang-Ulukus ‘12] Jing Yang and Sennur Ulukus, Optimal Packet Scheduling in an Energy Harvesting Communication System, IEEE Trans. on Communications, January 2012. § [Tutuncuoglu-Yener ’12a] Kaya Tutuncuoglu and Aylin Yener, Optimum Transmission Policies for Battery Limited Energy Harvesting Nodes, IEEE Trans. Wireless Communications, 11(3): 1180-1189, March 2012. § [Ozel et. al. ‘11] Omur Ozel, Kaya Tutuncuoglu, Jing Yang, Sennur Ulukus and Aylin Yener, Transmission with Energy Harvesting Nodes in Fading Wireless Channels: Optimal Policies, IEEE Journal on Selected Areas in Communications: Energy-Efficient Wireless Communications, 29(8):1732-1743,September 2011. § [Tutuncuoglu-Yener ’15] Kaya Tutuncuoglu, Aylin Yener, and Sennur Ulukus, Optimum Policies for an Energy Harvesting Transmitter Under Energy Storage Losses, IEEE Journal on Selected Areas in Communications: Wireless Communications Powered by Energy Harvesting and Wireless Energy Transfer, 33(3), pp. 467-481, Mar. 2015. § [Devillers-Gunduz ‘11]: Bertrand Devillers and Deniz Gunduz, A general framework for the

• ptimization of energy harvesting communication systems with battery imperfections, Journal
• f Communications and Networks, 14(2):130–139, April 2012.

§ [Tutuncuoglu-Yener ‘12b] Kaya Tutuncuoglu and Aylin Yener, Sum-Rate Optimal Power Policies for Energy Harvesting Transmitters in an Interference Channel, JCN Special issue on Energy Harvesting in Wireless Networks, 14(2), pp. 151–-161, Apr. 2012.

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References

References

§ [Gurakan-Ozel-Ulukus ’12]: Berk Gurakan, Omur Ozel, Jing Yang and Sennur Ulukus, Energy Cooperation in Energy Harvesting Communications, IEEE Trans. on Communications, 61(12): 4884-4898, December 2013. § [Tutuncuoglu-Yener ’13]: Kaya Tutuncuoglu and Aylin Yener, Multiple Access and Two-way Channels with Energy Harvesting and Bidirectional Energy Cooperation, Proceedings of the Information Theory and Applications Workshop, ITA'13, San Diego, CA, Feb. 2013. § [Tutuncuoglu-Ozel-Yener-Ulukus ’13]: Kaya Tutuncuoglu, Omur Ozel, Aylin Yener and Sennur Ulukus, Binary Energy Harvesting Channel with Finite Energy Storage, Proceedings of the IEEE International Symposium on Information Theory, ISIT'13, Istanbul, Turkey, Jul. 2013. § [Tutuncuoglu-Ozel-Yener-Ulukus ’14]: Kaya Tutuncuoglu, Omur Ozel, Aylin Yener, and Sennur Ulukus, Improved Capacity Bounds for the Binary Energy Harvesting Channel, Proceedings of the IEEE International Symposium on Information Theory, ISIT'14, Honolulu, HI, Jul. 2014. § [Tutuncuoglu-Ozel-Yener-Ulukus ’14]: Kaya Tutuncuoglu, Omur Ozel, Aylin Yener, and Sennur Ulukus, The Binary Energy Harvesting Channel with Unit Sized Battery, Transactions on IEEE Information Theory, accepted March 2017.

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