energy harvesting wireless communicationsulukus/papers/tutorials/icc13-part1-yener.pdf · energy...

Energy Harvesting Wireless Communications

Aylin Yener

[email protected]

IEEE ICC Tutorial PresentationBudapest, Hungary June 9, 2013

Outline1. Classical Networks

SIR-based design

Capacity-based design [Preliminary for Part 2]

2. Energy Harvesting Networks

Transmission Completion Time Minimization for single link

Short Term Throughput Maximization for single link with finite battery

Transmission Completion Time Minimization for single link w/ finite battery

Extension to fading channels

Transmission policies with inefficient energy storage

6/9/2013IEEE ICC 2013, Budapest, Hungary

Goals Energy Efficiency (EE): What it meant last decade;

what it means today

From a communication network design perspective what

should we care about for energy efficient design of cellular/conventional wireless networks? (greenish)

rechargeable/energy harvesting networks? (green)

Communication with energy harvesting nodes Green, self-sufficient nodes with extended network lifetime

Relatively new field with increasing interest6/9/2013

IEEE ICC 2013, Budapest, Hungary

Prerequisites for the Tutorial

Optimization (Basic) Communication Theory (Basic) Fairly self-contained otherwise



SIR-based design









Classical Networks

Multiple User/shared

frequency resources

(interference limited)

Battery powered mobile nodes

Single charge


Applications

Cellular Networks (nG, n>1) including multi-tier

(femto+macro) & network MIMO

Sensor networks (shared bandwidth, single or

multiple “sinks”)

Adhoc networks with “access” points

Multimedia traffic, we will concentrate on the

portion that is “energy hungry” = delay intolerant


Performance Measure

Quality of Service (QoS)

Packet delay

Delay sensitive applications (e.g. voice)

Packet error rate

Certain requirements to meet for quality


Performance Measure

Packet Error Rate

Bit Error Rate

SNR / SIR

Coding/Retransmission

Detection


Signal-to-Interference Ratio (SIR)

Performance Measure

ij jj

iii hp

hpSIRreceiver at power noise

user for tcoefficien channel user of power transmit

:::

ih

ip

i

i

Goal (EE): For acceptable SIR satisfying

QoS constraints, minimize total

transmission power in the network.


Interference Management for CDMA/SDMA systems

Users have unique, but non-orthogonal

signatures

Near-far problem

t

)(ts j

t

)(tsi


Near-Far Problem

Strong user can destroy weak user’s communication

ipih

jpjh

iijj hphp

Prominent in CDMA/SDMA systems(users share the same frequency and time)


Near-Far Problem

CDMA

ip ih

jpjh

iijj hphp

t

)(tsi

t

)(ts j

SDMA

ip

ihjp jh

iijj hphp

Better user with close code s(t) interferes

Better user with close spatial position interferes


Interference Management Techniques

Power Control [Yates’95]

Multiuser Detection/ Receiver Design [Verdu’98]

Adaptive Sectorization [Saraydar-Yener’01]

Transceiver (Precoder+Receiver) Design [Serbetli-

Yener’04]

EE Network design: Find the minimum power needed

with optimum receivers and/or transmitters.6/9/2013


SIR-based Power Control

pj (t 1) j

SIRj (t)pj (t)

Measure SIR

user j

user i

Base station

Feedback to users


[Yates ‘95]

Power Control + Receiver Design (SIMO)

)(tai

)(ta j

)(tr

R

Xi

user j

user i

sgn

Xk sgn

Xj sgn

……

BASE STATION

ib̂

kb̂

jb̂

)(1 tr

)(2 tr

)(trK…

chip sample

chip sample

chip sample

1r

2r

Kr

Feedback to users

)(ts j

)(tsi


[Yener et. al. ‘01]

Power Control + Transceiver Design (MIMO)

)(tai

user i

BASE STATION

ib̂

kb̂

jb̂

)(1 tr

)(2 tr

)(trK

… Receiver

Feedback to users

)(tsi


jHUSER j

Precoders

[Serbetli-Yener ‘04]

Capacity-Based Power Control

Fading: random fluctuations in channel gains.

CSI known both at the transmitter and the receiver

Ergodic capacity subject to average power

constraints

Main operational difference:

QoS based power control: compensate for channel effects

Capacity-based power control: exploit the channel effects


Single-User Fading Channel Channel capacity for single user

In the presence of fading, the capacity for channel state h,

Ergodic (expected) capacity under an average power constraint

C 12

log(1 SNR) 12

log 1 P 2

2

)(1log21)(

hhphC

hhpPhpts

hhp

h

hhp

,0)()(..

)(1log21max 2)(

E

E

[Goldsmith-Varaiya 97]6/9/2013


Optimal Power Allocation using Waterfilling

The Lagrangian

Optimality conditions

Complementary slackness condition:

Optimal Power Allocation:

dhhfhPhphhp

hh )()())(()(1log 2

EE

0)(

1)(0)(

*

2**

hph

hphp

Otherwise

then If

)(

)()( 2* hf

hhhph hhf of PDF the is where )(

hhph all for 0)()( *

(Water-filling)


Optimal Power Allocation using Waterfilling

Waterfilling of power over time:

hhp

2* 1)(


Illustration of Water-filling over Inverse of Channel States

Single User Optimum Power Allocation vs. Fading States

Differences Between QoS-Based and Capacity-Based Power Control

Single user system:

SIR-based:

Channel inversion; more power if channel is bad, less if channel is good. Compensate for channel fading via power control

Capacity-based:

Waterfilling; more power if channel is good, less if channel is bad. Exploit variations, opportunistic transmission

hhphhp 2

2 )()(

nxhy

hhphhp

h

2*

2

1)()(1logmax

E



SIR-based design





Transmission Completion Time Minimization for single link w/ finite

battery




Introduction

UbiquitousMobile / Remote Energy-

limited

Many sources

Abundant energy

Green

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.


Some Applications

Wireless sensor networks

Greencommunications


Motivation New Wireless Network Design Challenge:

A set of energy feasibility constraints based on 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


Two Main Goals of Transmission Scheduling

Transmission Completion Time Minimization (TCTM):

Given a number of bits to send, minimize the time at

which all bits have departed the transmitter.

Short-Term Throughput Maximization (STTM):

Given a deadline, maximize the number of bits sent

before the end of transmission.6/9/2013



SIR-based design









[Yang-Ulukus ‘12] System Model:

Energy harvesting transmitter Energy and data arrivals to transmitter Transmitting with power p achieves rate r(p)

TCTM for Single Link

Ei

Bi

transmitter receiver

Energy queueData queue


Energy harvests: Size Ei at time ti

Data packet arrivals: Size Bi at time si


System Model:E0

B0

t

TE1 E2 E3

B1 B2 B3

t1 t2 t3

s1 s2 s3s0

All arrivals known by transmitter beforehand.


Problem:Find optimal transmission power/rate policythat minimizes transmission time for a known amount of arriving packets.

Constraints:Cannot use energy not harvested yet.Cannot transmit packets not received yet.



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

1( ) log(1 )2

Pr PN


Power-Rate Function

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

)( pr

Rate

Power

pppr in decreasinglly monotonica is )()tan(

Given a fixed energy, a longertransmission with lower power departs more bits (Lazy Scheduling).

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


Transmission structure: Power pi for duration li

Expended Energy:

Departed bits:

Scenario I:Packets Ready before Transmission

E(t) pili pi1 t lii1

i

i1

i

, i max i : l j tj1

i B(t) r(pi )li r(pi1) t li

i1

i

i1

i

E0

B0

t

TE1 E2 EK

0

s1 s2 sK

p1

l1

p2

l2

pN

lN

…


Problem Definition:

Scenario I:Packets Ready before Transmission

0

:

)(

0 )( s.t. min

BTB

TtEtET

tsii

i

E0

B0

t

TE1 E2 EK

0

s1 s2 sK

p1

l1

p2

l2

pN

lN

…


Lemma 1: Transmit powers increase monotonically,

i.e.,

Proof: (by contradiction) assume not, i.e., for some i

Energy consumed in and is

Consider the following constant power policy:

which does not violate energy constraint since

Necessary conditions for optimality

Nppp ...21

1 ii pp

1 ii ll 11 iiii lplp

1

111

ii

iiiiii ll

lplppp

ii pp


Lemma 1: Transmit powers increase monotonically,

i.e.,

Proof(cont’d): Transmitted bits then become

where inequality is due to strict concavity of r(p)

Therefore pi>pi+1 cannot be optimal


Nppp ...21

ri li ri1li1 r pili pi1li1

li li1

(li li1)

r(pi )li

li li1

(li li1) r(pi1) li1

li li1

(li li1)

r(pi )li r(pi1)li1


Lemma 1: The transmit powers increase

monotonically, i.e.,

Proof(cont’d):


Nppp ...21

)( prRate

Powerip ip1ip

)(1

1 pll

l

ii

i

)(1

1 pll

l

ii

i

Time-sharing between

any two points is

strictly suboptimal for

concave r(p)


Lemma 2: The transmission power remains constant

between energy harvests.

Proof: (by contradiction) assume not

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.


],[ 1ii ss totalE

ist

],[ , 11

iiii

total sstss

Ep


E0

B0

t

TE1 E2 EK

0

s1 s2 sK

p1

l1

p2

l2

pN

lN

…

E0

B0

t

TE1 E2 EK

0

s1 s2 sK

p1

l1

p2

l2

pN

lN

…

Lemma 2: The transmission power remains constant

between energy harvests.


Transmission power only changes at is


Lemma 3: Whenever transmission rate changes,

energy buffer is empty.

Proof: (by contradiction) assume not, i.e., for some i

and energy buffer has energy remaining at time of change.


1 ii pp

Choose i and i1 such that ili i1li1 and let pi pi i , pi1 pi1 i1

Since amount of energy has moved from i 1 to i, and this was available at the buffer, this policy is feasible.


Lemma 3: Whenever transmission rate changes,

energy buffer is empty.


i1

)( prRate

Powerip ip 1ip1ip

i


Summary:

L1: Power only increases

L2: Power constant between arrivals

L3: At time of power change, energy buffer is empty

Conclusion:


For optimal policy, compare and sort (L1) power levels

that deplete energy buffer (L3) at arrival instances (L2).


Optimal Policy for Scenario I

For a given B0 the optimal policy satisfies:

and has the form

N

nnn Blpr

10)(

1

1

1

1

1

1

,

minarg

,...,2,1

1

1

:

nn

nn

n

n

n

n

nii

i

iinii

i

ij jn

ii

i

ij j

ssTsin

sslss

Ep

ss

Ei

Nn

for


1.

Algorithm for Scenario I

Find minimum number of energy arrivals required imin

by comparing: Ai r1 B0

si

si Ejj0

i1

Find simin1 T1 simin satisfying B0 r

Ejj0

i1T1

p1

si T1

111

min

1

011

1

,...1,,~min

pisl

iis

Epp

i

i

i

j j

of minimizer the is where

Set

2.

3.

4.1i

s from starting Repeat


Illustration – Step 1

E0

t

T1

E1 E2 EK

0 s1 s2 sK

A1

…

E3

s3

E4

s4

iE

t

A2A3

A4

Ai r1 B0

si

si Ejj0

i1



E0

t

T1

E1 E2 EK

0 s1 s2 sK…

E3

s3

E4

s4

iE

t

B0 rEjj0

i1T1

p1

si T1

1~p



E0

t

T1

E1 E2 EK

0 s1 s2 sK…

E3

s3

E4

s4

iE

tl1

p1

min

1

011 ...1,,~min ii

s

Epp

i

i

j j



E0

t

E1 E2 EK

0 s1 s2 sK…

E3

s3

E4

s4

iE

tl1

p1

T2 T3

p2

l2

p3

l3 T


Scenario II:Packets Arrive During Transmission

E0

B0

t

TE1 E2 EK

B1 B2

t1 t2

s1 s2 sKs0

Transmitter cannot depart packets not received yet!

Additional packet constraints apply


Scenario II:Packets Arrive During Transmission

Expended Energy:

Departed bits:

Problem Definition:

M

ii

ttii

tsii

BTB

TtBtB

TtEtET

i

i

0

:

:

)(

0 )(

0 )( s.t.min

E(t) pili pi1 t lii1

i

i1

i

, i max i : l j tj1

i B(t) r(pi )li r(pi1) t li

i1

i

i1

i

Energy Causality

Packet Causality


Lemma 4: Power only increases.

Lemma 5: Power constant between 2 arrivals of any kind.

Lemma 6: At time of power change:

(Proofs are similar to Lemmas 1-3)


if t si (energy arrival), energy buffer is empty;if t ti (packet arrival), packet buffer is empty.


Optimal Policy for Scenario II

The optimal policy satisfies

and has the form

M

ni

N

nnn Blpr

11)(

r(p1) mini:uiT

rEjj:s jui

ui

,Bjj:t jui

ui

yiterativel found are rates subsequent and

and ofncombinatio ordered the is where iii ts u



SIR-based design









[Tutuncuoglu-Yener ’12a] Maximize the throughput of an energy

harvesting transmitter by deadline T. Find optimal power allocation/transmission

policy that departs maximum number of bits in a given duration.

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

STTM for single link with Finite Battery


Energy arrivals of energy at times

Arrivals known non-causally by transmitter, Stored in a finite battery of capacity , Design parameter: power rate .

System Model

iE is

maxE)( pr

E0

t

TE1 E2 E3

s1 s2 s3s0


Notations and Assumptions

Power allocation function:

Energy consumed:

Short-term throughput:

Power-rate function r(p): Strictly concave in p Overflowing energy is lost (not optimal)

T

dttpr0

))((

)(tp

T

dttp0

)(


Battery Capacity:

Energy Constraints

(Energy arrivals of Ei at times si)

Energy Causality: nn

n

k

t

k stsdttpE

' 0)( 1

1

0

'

0

nn

n

k

t

k stsEdttpE

' )( 1

1

0

'

0 max

nn

n

k

t

k stsnEdttpEtp ' ,0 ,)(0 )( 1

1

0

'

0 max

Set of energy-feasible power allocations


Energy “Tunnel”

cE

t1s 2s

0E1E

2EmaxE

Energy Causality

Battery Capacity


STTM Problem for Single Link

Maximize total number of transmitted bits by deadline T

Convex constraint set, concave maximization problem

T

tptptsdttpr

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

nn

n

k

t


1

0

'

0 max


Necessary conditions for optimality of a transmission policy

Property 1: Transmission power remains constant between

arrivals.

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

)(

],[)()(



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.

Proof:

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

elsetptptp

tp

pp

TT

of concavity strict to due Then

depleted is batteryunless Feasible

Define

Let

00

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

)(

)()(






Policy can be improved Policy cannot be improved

p(t)

p’(t)p*(t)

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






Proof:


elsetptptp

tp

pp

TT

of concavity strict to due Then

full is batteryunless Feasible

Define

Let

00

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

)(

)()(






Policy can be improved Policy cannot be improved

p(t)p’(t)

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

p*(t)



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

Proof:

increasing is since Then

Define

p(t) after remains of energy an Assume


elsetp

TTtptp

TT

00

)(

],[)()(


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).

constant ,}{ ,0

)( 1nnn

nnn psiTt

itiptp


Energy “Tunnel”

cE

t1s 2s

0E1E

2EmaxE

Energy Causality

Battery Capacity


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)(max0

2

)(tptsdttp

T

tp

)( .. 1)(min0

2

)(tptsdttp

T

tp

length of policy path in energy tunnel


Shortest Path Interpretation

Property 1: Constant power is better than any other alternative

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

E

t06/9/2013


Throughput Maximizing Algorithm (TMA)

max1

1maxmax1110

0

',...,0for ,' ,'

,' ,' ,.'

11

1

nnissEE

nnniTTpiEE

nnnnnn

n

kk

Knowing the structure of the policy, we can construct an iterative

algorithm to get the tightest string in the tunnel.

Note: After a step is determined, the rest of the policy is

the solution to a shifted problem with shifted arrivals and deadline:

Essentially, the algorithm compares and find the tightest segment

that hits the upper or lower wall staying feasible all along.

),( 11 ip



]}[{][

]][],[[][

][

0,max][

max0max

0max

1

00

max0max

npn

npnpn

sE

np

sEE

np

n

n

k k

n

n

k k

P

PP[n]

p0[n]

pmax[n]

0E

E

1E

2EmaxE

t



},...,2,1, ][|max{ max1

nnknnn

kub

P

The transmission power must changebefore arrival nub+1 to stay in the feasible tunnel

nub=20E

E

1E

2E

maxE

t

At or before nub, battery must be empty or full to allow the necessary change. (Prop. 3)

Upper bound for the duration of the first step


1. Find . If terminate with power

2. Determine relation between

3. Transmit based on the outcome of step 2 with:

4. Repeat for shifted problem with updated parameters:

ubn maxnnub TEn

k k /) ( max

0

][ and ]1[ 0 kn ubnkub PP

11

101

001

][]}[][|max{

n

nk

sinpp

knpnn

P

11

1max1

0max1

][]}[][|max{

n

nk

sinpp

knpnn

P

max1

1maxmax1110

0

',...,0for ,' ,'

,' ,' ,.'

11

1

nnissEE

nnniTTpiEE

nnnnnn

n

kk



Alternative Solution

Transmission power is constant within each epoch:

STTM problem expressed with above notation

lEpLEts

prL

l

iiii

NM

iiipi

0 ..

)(.max

max1

1

1

}1...,,1 ,epoch {)( MNiitptp i

Energy constraints:sufficient to check

arrivals only(Li: length of epoch i)


Water-filling approach

Lagrangian function for STTM

KKT Stationarity Condition

Li .r(pi )

i1

M N1

j Li pi Eii1

j

j1

M N1

j Ei Li pi Emaxi1

j

j1

M N1

0 at p p *

1

1 1max

1

1 1

1

1)(.max

NM

j

j

iiiij

NM

j

j

iiiij

NM

iiip

EpLE

EpLprLi

jEpLE

jEpL

j

iiiij

j

iiiij

0

0

1max

1

(Complementary slackness conditions)


(Water Filling)1)(

1

)(1

1

01

1

0)()()(.

0)(.

1*

1

*

11

*

1

1

0

1

1

1

0

1

1

1

1

1

1 1max

1

1 1

1

1

)(

NM

kj jjk

NM

kjjj

k

NM

kjjk

NM

kjjk

kk

NM

j

kjifkjifL

j

iikij

NM

j

kjifkjifL

j

iikij

NM

i

p

iki

NM

j

j

iiiij

NM

j

j

iiiij

NM

iiik

p

p

LLp

L

pLpLprL

nEpLEEpLprL

kki

ki

Water-filling approach Gradient for kth component


0

0

1max

1

j

iiiij

j

iiiij

EpLE

EpL

full is battery when only positive only 's

empty is battery when only positive are 's

Water-filling approach

Complementary Slackness

Conditions: jEpLE

jEpL

j

iiiij

j

iiiij

0

0

1max

1

j

jNM

kj jjkp

positive a at increases positive a at decreases

1)(

11

*


Directional Water-Filling

Harvested energies filled into epochs individually

0 tO O O

0E 1E 2E

Water levels (vi)




Constraints:

Energy Causality: water-flow only forward in time

0 tO O O

0E 1E 2E

Water levels (vi)




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)



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



Energy tunnel

and directional

water-filling

approaches

yield the same

policy

E

t0

0 tO O O OO O


Simulation Results

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



SIR-based design









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

Transmission Completion Time Minimization (TCTM) for single link with finite battery

T

tptpdttprBtsT

0)()(,0))((..min

nn

n

k

t


1

0

'

0 max


maxu0

minT

T uB u.maxp(t )P

r(p(t))dt0

T

Lagrangian dual of TCTM problem becomes:

Relationship ofSTTM and TCTM problems

T

TPtpudttprBuT

0,)(0))(( minmax

STTM problem for deadline T


Optimal allocations are identical:

STTM solution can be used to solve the TCTM problem

Relationship ofSTTM and TCTM problems

STTM’s solution for deadline T

departing B bits

TCTM’s solution for departing Bbits in time T


Maximum Service Curve

1S 2S Deadline (T)3S

Max

imum

Dep

artu

re (

B) Maximum number of bits

that can be sent in time T.

Each point calculated by solving the corresponding STTM problem.

T

tptptsdttprTs

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



Continuous, monotone increasing, invertible

Optimal allocation for TCTM with B1bits

Optimal allocation for STTM with deadline T1

1S 2S Deadline (T)3S

Max

imum

Dep

artu

re (

B)

T1

B1



SIR-based design









Extension to Fading Channels

[Ozel et. al. ‘11]

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

Finite battery capacity


System Model

AWGN Channel with fading h :

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

Fading states and harvests known non-causally

).1log(21),( PhhPR

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


STTM Problem with Fading

Transmission power constant within each epoch:

Maximize total number of transmitted bits by a

deadline T

lEpLEts

phL

l

iiii

NM

iii

i

pi

0 ..

)1log(2

max

max1

1

1

p(t) {pi , t epoch i, i 1,..., N M 1}



Lagrangian of the STTM problem

i

NM

ii

NM

j

j

iiiij

NM

j

j

iiiij

NM

iii

i

p

pEpLE

EpLphLi

1

1

1

1 1max

1

1 1

1

1)1log(

2max

jp

jEpLE

jEpL

jj

j

iiiij

j

iiiij

0

0

0

1max

1

(Complementary slackness conditions)

Solution: directional water-filling with

fading levels:

1

* 1 ,1NM

ij jji

iii v

hvp


(Water Filling)

kNM

kj jjk

kkk

NM

kjjj

kk

k

k

NM

kjjk

NM

kjjk

kk

kk

ik

NM

ii

NM

j

kjifkjifL

j

iikij

NM

j

kjifkjifL

j

iikij

NM

i

phh

iki

i

NM

ii

NM

j

j

iiiij

NM

j

j

iiiij

NM

iiik

hp

ppph

h

LLph

hL

ppLpLprL

npEpLEEpLprL

kkkik

kik

1)(

1

000)(1

01

0)()()()(.

0)(.

1*

**1

*

11

*

1

1

1

1

0

1

1

1

0

1

1

1

1

1

1

1

1 1max

1

1 1

1

1

)(

) and Otherwise satisfied. is (if




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)



Same directional water filling model with added

fading levels.

Directional water flow (Energy causality)

Limited water flow (Battery capacity)

0 tO O Ox

→

0E→

2E→

4E

x

Water depth givestransmission power pi



Continuous, non-decreasing(flat regions when fading is severe)

Inverse can be considered as the smallest T that achieves B1

Deadline (T)

Max

imum

Dep

artu

re (

B)

T1

B1

O x x x x x xO O O


Online AlgorithmsOptimal online policy can be found using dynamic

programming States of the system: fade level: h, battery energy: e

Quantizing time by δ, g*(e,h,kδ) can be found by iteratively solving

gg

T

tg

JtheJ

dheghEtheJ

sup),,(

)),,()(1log(21),,(

),','()),,(.1log(

2max

),,( theJthegh

theg

)](|)(['

)),,(('ththEhPthegee avg


Online AlgorithmsConstant Water Level

A cutoff fading level h0 is determined by the average harvested power Pavg as:

Transmitter uses the corresponding water-filling power if available, is silent otherwise

ii hh

p 11

0

1h0

1h

h0

f (h)dh Pavg f(h): Fading distribution


Online AlgorithmsTime-Energy Adaptive Water-filling h0 determined by remaining energy scaled by remaining time as

Hybrid Adaptive Water-filling h0 determined similarly but by adding average received power

1h0

1h

h0

f (h)dh Ecurrent

T t

1h0

1h

h0

f (h)dh Ecurrent

T t Pavg


Simulations

Performances of the policies w.r.t. energy arrival rates under:

unit mean Rayleigh fading

T = 10 sec

Emax = 10 J.



SIR-based design









Transmission Policies with Inefficient Energy Storage

Energy stored in a battery, supercapacitor, . . .

“Real life” issues:

[Devillers-Gunduz ‘11]: Leakage and Degradation

[Tutuncuoglu-Yener ‘12b]: Storage/Recovery Losses


Storage Loss

LeakageDegradation

Recovery Loss

Battery Degradation

[Devillers-Gunduz ‘11]

Optimal Policy: Shortest path within narrowing tunnel


Degradation

E

t0

Battery Leakage

[Devillers-Gunduz ‘11]

Optimal Policy: When total energy in an epoch is low, deplete

energy earlier to reduce leakage.


E

t0

Leakage

Storage/Recovery Losses

[Tutuncuoglu-Yener ’12b]

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


h(t)Transmitter Receiver

Energy storage (ESD)

Emax

s(t)η u(t)

p(t) = h(t) – s(t) + u(t)

System Model

Rate: r(p(t))

h(t): Harvested power s(t): Stored power u(t): Retrieved (used) power p(t): Transmit power

ESD has finite capacity Emax and storage efficiency η.

Energy Causality:

Storage Capacity:

Tt,dust

00)()(0

Tt,Edust

0)()( max0

Find optimal energy storage policy that maximizes the average transmission rate of an energy harvesting transmitter within a deadline T.

Average Rate Maximization


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

)()( 0 ..

))()()((1 max

max0

0)(),(

Tttutsth

Edusts

dttutsthrT

t

T

tuts

.0 ,0)(

)()( 0 ..

))((1 max

max0

0)(),(

Tttp

Edphts

dttprT

t

T

tuts

Original problem

Optimal Power Policy


Tttuttst

EtEt

ust

bat

tE

t

bat

0,0)()(,0)()(,0))(()(

,0)()()(

max

)(

0

Tttdtpr

tdtprT

t

T

t

0,0)()())(('

,0)()()())(('

KKT

Stationarity

Complementary

Slackness

When battery is charging (s(t)>0)

When battery is discharging (u(t)>0)


T

tdtpr )()())(('

T

tdtpr

)()(1))(('

)(')('

u

s

prpr


“Double Threshold Policy”

uu

su

ss

pthppthpth

pthptp

)()()(

)()(

)(tp

0

up

sp

)(th


p

)(th

)(tp

T t

sp

up

1t0


6/9/2013 IEEE ICC 2013, Budapest, Hungary

Optimal Online Algorithm

Optimal online policy

turns out to be a

double threshold

policy with adaptive

thresholds (as a fct

of battery states)

))](),(([)),((sup),( thteJhegrheJg

E

User has causal energy harvesting information only

Fix the thresholds throughout the transmission

to satisfy

Near-Optimal Online Algorithm


and

and

0)()()()(

)()()(

max

tEpthppthpth

EtEpthptp

batouou

osou

batosos

ou

os

p

houp hos dppfppdppfpp0

)()()()(

Simulations


Conclusion

• In this tutorial, we covered energy efficient design for classical (single charge) networks, as well as optimal scheduling policies for one Energy Harvesting (rechargeable) transmitter.

• New networking paradigm: energy harvesting nodes New design insights arise from new energy

constraints! Lots of open problems related to all layers of the

network design: e.g. Signal processing/PHY design; MAC protocol design ; Channel capacity…


Acknowledgements

NSF CNS 0964364 Slides: Kaya Tutuncuoglu


ReferencesClassical Networks [Yates ’95] R. Yates. A framework for uplink power control in cellular radio

systems. IEEE Journal on Selected Areas of Communications, 13(7):1341-1348, September 1995.

[Verdu’98] S. Verdu. Multiuser Detection. Cambridge, 1998. [Saraydar-Yener ‘01] C. Saraydar and A. Yener. Adaptive Cell Sectorization for

CDMA Systems., IEEE Journal on Selected Areas in Communications, 19(6):1041-1051, June 2001.

[Yener et. al. ‘01] A. Yener, R. Yates, and S. Ulukus. Interference management for CDMA systems through power control, multiuser detection and beamforming, IEEE Trans. on Communications, 49(7):1227-1239, July 2001.

[Serbetli-Yener ‘04] Semih Serbetli and Aylin Yener,Transceiver Optimization for Multiuser MIMO Systems, IEEE Trans. on Signal Processing, 52(1):214-226, January 2004.

[Goldsmith-Varaiya ‘97]A. Goldsmith and P. Varaiya, Capacity of fading channels with channel side information , IEEE Trans. on Information Theory, 43(11): pp., November 1997.


ReferencesEnergy Harvesting Networks [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 ’12b] Kaya Tutuncuoglu and Aylin Yener, Communicating Using an Energy Harvesting Transmitter: Optimum Policies Under Energy Storage Losses, IEEE Trans.Wireless Communications, submitted August 2012, available at arXiv:1208.6273v1, conference version at CISS 2012.

[Devillers-Gunduz ‘11]:B. Devillers and D. Gunduz, A general framework for the optimization of energy harvesting communication systems with battery imperfections, Journal of Communications and Networks, 14(2):130–139, April 2012.


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