Energy Harvesting Wireless Communications
Aylin Yener
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
6/9/2013IEEE ICC 2013, Budapest, Hungary
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
Classical Networks
Multiple User/shared
frequency resources
(interference limited)
Battery powered mobile nodes
Single charge
6/9/2013IEEE ICC 2013, Budapest, Hungary
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
6/9/2013IEEE ICC 2013, Budapest, Hungary
Performance Measure
Quality of Service (QoS)
Packet delay
Delay sensitive applications (e.g. voice)
Packet error rate
Certain requirements to meet for quality
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Performance Measure
Packet Error Rate
Bit Error Rate
SNR / SIR
Coding/Retransmission
Detection
6/9/2013IEEE ICC 2013, Budapest, Hungary
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.
6/9/2013IEEE ICC 2013, Budapest, Hungary
Interference Management for CDMA/SDMA systems
Users have unique, but non-orthogonal
signatures
Near-far problem
t
)(ts j
t
)(tsi
6/9/2013IEEE ICC 2013, Budapest, Hungary
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)
6/9/2013IEEE ICC 2013, Budapest, Hungary
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
6/9/2013IEEE ICC 2013, Budapest, Hungary
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
IEEE ICC 2013, Budapest, Hungary
SIR-based Power Control
pj (t 1) j
SIRj (t)pj (t)
Measure SIR
user j
user i
Base station
Feedback to users
6/9/2013IEEE ICC 2013, Budapest, Hungary
[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
6/9/2013IEEE ICC 2013, Budapest, Hungary
[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
6/9/2013IEEE ICC 2013, Budapest, Hungary
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
6/9/2013IEEE ICC 2013, Budapest, Hungary
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
IEEE ICC 2013, Budapest, Hungary
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)
6/9/2013IEEE ICC 2013, Budapest, Hungary
Optimal Power Allocation using Waterfilling
Waterfilling of power over time:
hhp
2* 1)(
6/9/2013IEEE ICC 2013, Budapest, Hungary
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
6/9/2013IEEE ICC 2013, Budapest, Hungary
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
Introduction
UbiquitousMobile / Remote Energy-
limited
Many sources
Abundant energy
Green
Energy
Harvesting
Wireless
Networks
6/9/2013IEEE ICC 2013, Budapest, Hungary
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.
6/9/2013IEEE ICC 2013, Budapest, Hungary
Some Applications
Wireless sensor networks
Greencommunications
6/9/2013IEEE ICC 2013, Budapest, Hungary
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
6/9/2013IEEE ICC 2013, Budapest, Hungary
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
IEEE ICC 2013, Budapest, Hungary
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
[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
6/9/2013IEEE ICC 2013, Budapest, Hungary
Energy harvests: Size Ei at time ti
Data packet arrivals: Size Bi at time si
TCTM for Single Link
System Model:E0
B0
t
TE1 E2 E3
B1 B2 B3
t1 t2 t3
s1 s2 s3s0
All arrivals known by transmitter beforehand.
6/9/2013IEEE ICC 2013, Budapest, Hungary
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.
TCTM for Single Link
6/9/2013IEEE ICC 2013, Budapest, Hungary
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
6/9/2013IEEE ICC 2013, Budapest, Hungary
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
6/9/2013IEEE ICC 2013, Budapest, Hungary
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
…
6/9/2013IEEE ICC 2013, Budapest, Hungary
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
…
6/9/2013IEEE ICC 2013, Budapest, Hungary
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
6/9/2013IEEE ICC 2013, Budapest, Hungary
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
Necessary conditions for optimality
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
6/9/2013IEEE ICC 2013, Budapest, Hungary
Lemma 1: The transmit powers increase
monotonically, i.e.,
Proof(cont’d):
Necessary conditions for optimality
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)
6/9/2013IEEE ICC 2013, Budapest, Hungary
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.
Necessary conditions for optimality
],[ 1ii ss totalE
ist
],[ , 11
iiii
total sstss
Ep
6/9/2013IEEE ICC 2013, Budapest, Hungary
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.
Necessary conditions for optimality
Transmission power only changes at is
6/9/2013IEEE ICC 2013, Budapest, Hungary
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.
Necessary conditions for optimality
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.
6/9/2013IEEE ICC 2013, Budapest, Hungary
Lemma 3: Whenever transmission rate changes,
energy buffer is empty.
Necessary conditions for optimality
i1
)( prRate
Powerip ip 1ip1ip
i
6/9/2013IEEE ICC 2013, Budapest, Hungary
Summary:
L1: Power only increases
L2: Power constant between arrivals
L3: At time of power change, energy buffer is empty
Conclusion:
Necessary conditions for optimality
For optimal policy, compare and sort (L1) power levels
that deplete energy buffer (L3) at arrival instances (L2).
6/9/2013IEEE ICC 2013, Budapest, Hungary
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
6/9/2013IEEE ICC 2013, Budapest, Hungary
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
6/9/2013IEEE ICC 2013, Budapest, Hungary
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
6/9/2013IEEE ICC 2013, Budapest, Hungary
Illustration – Step 2
E0
t
T1
E1 E2 EK
0 s1 s2 sK…
E3
s3
E4
s4
iE
t
B0 rEjj0
i1T1
p1
si T1
1~p
6/9/2013IEEE ICC 2013, Budapest, Hungary
Illustration – Step 3
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
6/9/2013IEEE ICC 2013, Budapest, Hungary
Illustration – Step 4
E0
t
E1 E2 EK
0 s1 s2 sK…
E3
s3
E4
s4
iE
tl1
p1
T2 T3
p2
l2
p3
l3 T
6/9/2013IEEE ICC 2013, Budapest, Hungary
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
6/9/2013IEEE ICC 2013, Budapest, Hungary
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
6/9/2013IEEE ICC 2013, Budapest, Hungary
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)
Necessary conditions for optimality
if t si (energy arrival), energy buffer is empty;if t ti (packet arrival), packet buffer is empty.
6/9/2013IEEE ICC 2013, Budapest, Hungary
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
6/9/2013IEEE ICC 2013, Budapest, Hungary
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
[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
6/9/2013IEEE ICC 2013, Budapest, Hungary
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
6/9/2013IEEE ICC 2013, Budapest, Hungary
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
)(
6/9/2013IEEE ICC 2013, Budapest, Hungary
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
6/9/2013IEEE ICC 2013, Budapest, Hungary
Energy “Tunnel”
cE
t1s 2s
0E1E
2EmaxE
Energy Causality
Battery Capacity
6/9/2013IEEE ICC 2013, Budapest, Hungary
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
k stsnEdttpEtp ' ,0 ,)(0 )( 1
1
0
'
0 max
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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
)(
],[)()(
6/9/2013IEEE ICC 2013, Budapest, Hungary
Necessary conditions for optimality of a transmission policy
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
)(],[)(],[)(
)(
)()(
6/9/2013IEEE ICC 2013, Budapest, Hungary
Necessary conditions for optimality of a transmission policy
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(
6/9/2013IEEE ICC 2013, Budapest, Hungary
Necessary conditions for optimality of a transmission policy
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
full is batteryunless Feasible
Define
Let
00
)(],[)(],[)(
)(
)()(
6/9/2013IEEE ICC 2013, Budapest, Hungary
Necessary conditions for optimality of a transmission policy
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)
6/9/2013IEEE ICC 2013, Budapest, Hungary
Necessary conditions for optimality of a transmission policy
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
)(
],[)()(
6/9/2013IEEE ICC 2013, Budapest, Hungary
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
6/9/2013IEEE ICC 2013, Budapest, Hungary
Energy “Tunnel”
cE
t1s 2s
0E1E
2EmaxE
Energy Causality
Battery Capacity
6/9/2013IEEE ICC 2013, Budapest, Hungary
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
6/9/2013IEEE ICC 2013, Budapest, Hungary
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
IEEE ICC 2013, Budapest, Hungary
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
6/9/2013IEEE ICC 2013, Budapest, Hungary
Throughput Maximizing Algorithm (TMA)
]}[{][
]][],[[][
][
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
6/9/2013IEEE ICC 2013, Budapest, Hungary
Throughput Maximizing Algorithm (TMA)
},...,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
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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
Throughput Maximizing Algorithm (TMA)
6/9/2013IEEE ICC 2013, Budapest, Hungary
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)
6/9/2013IEEE ICC 2013, Budapest, Hungary
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)
6/9/2013IEEE ICC 2013, Budapest, Hungary
(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
6/9/2013IEEE ICC 2013, Budapest, Hungary
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
*
6/9/2013IEEE ICC 2013, Budapest, Hungary
Directional Water-Filling
Harvested energies filled into epochs individually
0 tO O O
0E 1E 2E
Water levels (vi)
6/9/2013IEEE ICC 2013, Budapest, Hungary
Directional Water-Filling
Harvested energies filled into epochs individually
Constraints:
Energy Causality: water-flow only forward in time
0 tO O O
0E 1E 2E
Water levels (vi)
6/9/2013IEEE ICC 2013, Budapest, Hungary
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
0 tO O O
0E 1E 2E
Water levels (vi)
6/9/2013IEEE ICC 2013, Budapest, Hungary
Directional Water-Filling
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
6/9/2013IEEE ICC 2013, Budapest, Hungary
Directional Water-Filling
Energy tunnel
and directional
water-filling
approaches
yield the same
policy
E
t0
0 tO O O OO O
6/9/2013IEEE ICC 2013, Budapest, Hungary
Simulation Results
Improvement of optimal algorithm over an on-off transmitter in a simulation with truncated Gaussian arrivals.
6/9/2013IEEE ICC 2013, Budapest, Hungary
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
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
k stsnEdttpEtp ' ,0 ,)(0 )( 1
1
0
'
0 max
6/9/2013IEEE ICC 2013, Budapest, Hungary
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
6/9/2013IEEE ICC 2013, Budapest, Hungary
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
6/9/2013IEEE ICC 2013, Budapest, Hungary
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)(
6/9/2013IEEE ICC 2013, Budapest, Hungary
Maximum Service Curve
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
6/9/2013IEEE ICC 2013, Budapest, Hungary
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
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
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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
6/9/2013IEEE ICC 2013, Budapest, Hungary
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}
6/9/2013IEEE ICC 2013, Budapest, Hungary
STTM Problem with Fading
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
6/9/2013IEEE ICC 2013, Budapest, Hungary
(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
STTM Problem with Fading
6/9/2013IEEE ICC 2013, Budapest, Hungary
Directional Water-Filling
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)
6/9/2013IEEE ICC 2013, Budapest, Hungary
Directional Water-Filling
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
6/9/2013IEEE ICC 2013, Budapest, Hungary
Maximum Service Curve
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
6/9/2013IEEE ICC 2013, Budapest, Hungary
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
6/9/2013IEEE ICC 2013, Budapest, Hungary
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
6/9/2013IEEE ICC 2013, Budapest, Hungary
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
6/9/2013IEEE ICC 2013, Budapest, Hungary
Simulations
Performances of the policies w.r.t. energy arrival rates under:
unit mean Rayleigh fading
T = 10 sec
Emax = 10 J.
6/9/2013IEEE ICC 2013, Budapest, Hungary
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
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
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Storage Loss
LeakageDegradation
Recovery Loss
Battery Degradation
[Devillers-Gunduz ‘11]
Optimal Policy: Shortest path within narrowing tunnel
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Degradation
E
t0
Battery Leakage
[Devillers-Gunduz ‘11]
Optimal Policy: When total energy in an epoch is low, deplete
energy earlier to reduce leakage.
6/9/2013IEEE ICC 2013, Budapest, Hungary
E
t0
Leakage
Storage/Recovery Losses
[Tutuncuoglu-Yener ’12b]
Main Tension:
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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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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
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.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
6/9/2013IEEE ICC 2013, Budapest, Hungary
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)
6/9/2013IEEE ICC 2013, Budapest, Hungary
T
tdtpr )()())(('
T
tdtpr
)()(1))(('
)(')('
u
s
prpr
Optimal Power Policy
“Double Threshold Policy”
uu
su
ss
pthppthpth
pthptp
)()()(
)()(
)(tp
0
up
sp
)(th
6/9/2013IEEE ICC 2013, Budapest, Hungary
p
)(th
)(tp
T t
sp
up
1t0
Optimal Power Policy
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
6/9/2013 IEEE ICC 2013, Budapest, Hungary
and
and
0)()()()(
)()()(
max
tEpthppthpth
EtEpthptp
batouou
osou
batosos
ou
os
p
houp hos dppfppdppfpp0
)()()()(
Simulations
6/9/2013 IEEE ICC 2013, Budapest, Hungary
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…
6/9/2013IEEE ICC 2013, Budapest, Hungary
Acknowledgements
NSF CNS 0964364 Slides: Kaya Tutuncuoglu
6/9/2013IEEE ICC 2013, Budapest, Hungary
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.
6/9/2013IEEE ICC 2013, Budapest, Hungary
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.
6/9/2013IEEE ICC 2013, Budapest, Hungary