METU - Ankara ECROPS: Minimum Energy with … - 2016.pdfMinimum Energy with Maximum Harvesting for...

ECROPS: Minimum Energy with Maximum

Harvesting for Optimal Communications

Erol Gelenbe

Intelligent Systems and Networks Group Department of Electrical and Electronic Engineering

Imperial College London

CTTC Barcelona

METU - Ankara

2020 ICT Carbon 1.43BTONNES CO2

2007 ICT = 0.83BTONNES CO2

~ Aviation = 2% Growth 4%

2

360m tons CO2

260m tons CO2

EU 2012 ICT = 4.7% of Electricity Worldwide

1000 TeraW-hrs/year > Japan’s Electricity

High-Level Contributions of ECROPS

Example Problem: Optimum Power to Minimse Energy Consumption per Successfully Received Data Packet

• Cooperating (Wireless) Transmitters

• Choose the Individual transmission power to Minimize the Energy Consumed per Correctly Received Packet

Power Level, Interference and Errors

• Identical Wireless Transmitters

• Transmit D packets at rate v: Transmission Time D/v

• Power Consumption P(v)

PElectronics+PTransm+ Packet Queue

Optimum Energy Efficiency vs Power

• Error Probability

• Effective Transmission Time

• Efficiency: Number of Effectively Transmitted Packets per Energy Unit (NOT Power Unit) PElectronics+PTransm+ Packet Queue

~ 1- f (rPT

B(noise) + Interference))

Teff =D

v. f (g), g =

rPT

B+ I

D-

(PT ) =D

(PE + PT ).Teff

= vf (

rPT

B+ I)

(PE + PT )

Generally f needs to be determined empirically, or with detailed analysis, but in simple cases:

- Single Bipolar Binary Bit +1,-1 Transmission

- Uncoded Block of n Bipolar Bits

- Where

γa γ∗

f

Fig. 2. Optimal transmission power for a generic function f in the presenceof fixed interference.

In the rest of the paper we normalize the transmission rate

and consider v = 1 for the sake of simplicity. To increase the

energy efficiency of the communication system, our goal is to

find the transmission power PT that maximizes the average

number of successfully transmitted packets per unit energy,

D (PT ). To simplify the notation, we define c B + Ir

. The

newly defined variable c ≥ 0 is the inverse of the channel

gain to interference plus noise ratio, which is a measure of

the channel quality. The optimization problem reduces to

max D (PT ) =f (γ)

PE + c · γfor γ ≥ 0. (4)

This can be solved by maximizing f (γ)/ (a + γ) with

a PE / c > 0, and the maximum value of D (PT ) is found

by dividing the result of this optimization by c. We assume

that the function f is continuously differentiable. Then the

necessary condition for the maximum value can be written as

d

dγ

f (γ)

a + γ=

1

a + γf (γ) −

f (γ)

a + γ= 0. (5)

Equivalently, the optimal SINR γ∗ should satisfy

(a + γ∗ )f (γ∗ ) = f (γ∗ ). (6)

We first note that when the power consumed by the pro-

cessing units is zero, i.e., PE = 0, and if f (0) > 0, then

the maximum energy efficiency is obtained by zero-power

transmission. For practical systems, it is reasonable to assume

that f (0) = 0, i.e., a packet cannot be received correctly if

there is no transmission. Under this assumption, we define

a new function g(x) f (x) − (a + x)f (x). We have

g(0) = − af (0) < 0. On the other hand, g(x) becomes

positive for sufficiently high values of x. This means that the

necessary condition in (6) always has a solution.

This condition can be visualized as in Figure 2, where we

draw tangents to the function f (·) from the point (− a, 0), and

the points where these tangents intersect the function are the

points for which thenecessary condition in (6) is satisfied. The

slope of each tangent line gives us the corresponding D (γ∗ )

value; and hence, the maximum slope among all the tangents,

the blue line in the figure, is the solution of the maximization

problem in (4).

A. BPSK Modulated Uncoded Transmission

Here we consider a specific transmission scheme and ana-

lyze the energy efficiency under this assumption. In particular,

we assume that each data packet consists of n independent

binary symbols, which are transmitted over the channel using

BPSK signalling without any coding.

Due to lack of coding, the receiver tries to decode each

binary symbol separately, and the data packet is assumed to be

decoded successfully only if all the bits are decoded correctly.

The probability of correctly decoding each binary symbol is

given by [31]

1− QrPT

B + αPT

.

Hence, the function f for this uncoded transmission scheme

is found as

f (x) = [1− Q (√

x)]n

.

Note that for this specific transmission scheme we have

f (0) = (1 − Q(0))n = 2− n > 0. Hence, under this

assumption the receiver can reconstruct the packet correctly

with a positive probability even if there is no transmission.

However, we can notice that as n increases f (0) quickly

approaches zero. Another observation regarding this special

transmission scheme is that the necessary condition in (6)

is satisfied at most two points, and the optimal transmission

power is given by the one that corresponds to the higher PT

value. Hence, the optimal transmission power is unique.

A closed-form expression for the optimal transmission

power P ∗T is elusive; while the solution can be found numer-

ically. In Figure 3 we assume PE = 2, and plot the function

f (·) for n = 100. We then find the optimal tangents to the

function for c = 2 and c = 0.4, which correspond to a = 1

and a = 5, respectively. Accordingly the optimal transmission

power values on the figure are found as the intersection points

of the tangents to the function f from points (− 5, 0) and

(− 1, 0).

We can see from the figure that the optimal number of

packets per unit energy D ∗ decreases as a or c increases.

In this example, we have D ∗ 0.0441, P ∗T = 16.6 and

D ∗ 0.1555, P ∗T = 3.66 for c = 2 and c = 0.4, respectively.

We observe that the optimal transmission power P ∗T increases

with c.

IV. MULTI-USER SCENARIO: INTERFERENCE SCALED

WITH TRANSMISSION POWER

Many communication theoretic results in the literature are

obtained by scaling the transmission power to infinity while

keeping the noise level constant; see, for example, [32], [33],

[34]. However, as it has been correctly pointed out in [35],

in practical scenarios, multiple systems operate in the same

medium interfering with each other. A realistic analysis of

the performance in these cases requires the scaling of the

interference together with the transmission power.

γa γ∗

f

Fig. 2. Optimal transmission power for a generic function f in the presenceof fixed interference.

In the rest of the paper we normalize the transmission rate

and consider v = 1 for the sake of simplicity. To increase the

energy efficiency of the communication system, our goal is to

find the transmission power PT that maximizes the average

number of successfully transmitted packets per unit energy,

D (PT ). To simplify the notation, we define c B + Ir

. The

newly defined variable c ≥ 0 is the inverse of the channel

gain to interference plus noise ratio, which is a measure of

the channel quality. The optimization problem reduces to

max D(PT ) =f (γ)

PE + c · γfor γ ≥ 0. (4)

This can be solved by maximizing f (γ)/ (a + γ) with

a PE / c > 0, and the maximum value of D (PT ) is found

by dividing the result of this optimization by c. We assume

that the function f is continuously differentiable. Then the

necessary condition for the maximum value can be written as

d

dγ

f (γ)

a + γ=

1

a + γf (γ) −

f (γ)

a + γ= 0. (5)

Equivalently, the optimal SINR γ∗ should satisfy

(a + γ∗ )f (γ∗ ) = f (γ∗ ). (6)

We first note that when the power consumed by the pro-

cessing units is zero, i.e., PE = 0, and if f (0) > 0, then

the maximum energy efficiency is obtained by zero-power

transmission. For practical systems, it is reasonable to assume

that f (0) = 0, i.e., a packet cannot be received correctly if

there is no transmission. Under this assumption, we define

a new function g(x) f (x) − (a + x)f (x). We have

g(0) = − af (0) < 0. On the other hand, g(x) becomes

positive for sufficiently high values of x. This means that the

necessary condition in (6) always has a solution.

This condition can be visualized as in Figure 2, where we

draw tangents to the function f (·) from the point (− a, 0), and

the points where these tangents intersect the function are the

points for which thenecessary condition in (6) issatisfied. The

slope of each tangent line gives us the corresponding D (γ∗ )

value; and hence, the maximum slope among all the tangents,

the blue line in the figure, is the solution of the maximization

problem in (4).

A. BPSK Modulated Uncoded Transmission

Here we consider a specific transmission scheme and ana-

lyze the energy efficiency under this assumption. In particular,

we assume that each data packet consists of n independent

binary symbols, which are transmitted over the channel using

BPSK signalling without any coding.

Due to lack of coding, the receiver tries to decode each

binary symbol separately, and thedatapacket isassumed to be

decoded successfully only if all the bits are decoded correctly.

The probability of correctly decoding each binary symbol is

given by [31]

1− QrPT

B + αPT

.

Hence, the function f for this uncoded transmission scheme

is found as

f (x) = [1− Q (√

x)]n

.

Note that for this specific transmission scheme we have

f (0) = (1 − Q(0))n = 2− n > 0. Hence, under this

assumption the receiver can reconstruct the packet correctly

with a positive probability even if there is no transmission.

However, we can notice that as n increases f (0) quickly

approaches zero. Another observation regarding this special

transmission scheme is that the necessary condition in (6)

is satisfied at most two points, and the optimal transmission

power is given by the one that corresponds to the higher PT

value. Hence, the optimal transmission power is unique.

A closed-form expression for the optimal transmission

power P∗T is elusive; while the solution can be found numer-

ically. In Figure 3 we assume PE = 2, and plot the function

f (·) for n = 100. We then find the optimal tangents to the

function for c = 2 and c = 0.4, which correspond to a = 1

and a = 5, respectively. Accordingly the optimal transmission

power values on the figure are found as the intersection points

of the tangents to the function f from points (− 5, 0) and

(− 1, 0).

We can see from the figure that the optimal number of

packets per unit energy D ∗ decreases as a or c increases.

In this example, we have D ∗ 0.0441, P∗T = 16.6 and

D ∗ 0.1555, P∗T = 3.66 for c = 2 and c = 0.4, respectively.

We observe that the optimal transmission power P∗T increases

with c.

IV. MULTI-USER SCENARIO: INTERFERENCE SCALED

WITH TRANSMISSION POWER

Many communication theoretic results in the literature are

obtained by scaling the transmission power to infinity while

keeping the noise level constant; see, for example, [32], [33],

[34]. However, as it has been correctly pointed out in [35],

in practical scenarios, multiple systems operate in the same

medium interfering with each other. A realistic analysis of

the performance in these cases requires the scaling of the

interference together with the transmission power.

Q(x) =1

2pe-t2

/2

x

¥

ò dt

Identical Multi-Users: Optimum Energy Efficiency vs Power


• Efficiency – Number of Packets Correctly transmitted per Unit of Energy

When I = a PT , We are only interested in f(x) with 0<x<r/a,

and the optimum PT that maximizes Efficiency satisfies

~ 1- f (rPT

B(noise) + Interference))

¶f (x)

¶x=

(B+ aPT )2

rB(PE + PT ). f (x), where x =

rPT

B +aPT

D-

(PT ) =D

(PE + PT ).Teff

= v

f (rPT

B+ aPT

)

(PE + PT )

Identical Multi-Users with n-bit un-encoded packets


• Energy Efficiency – Number of Packets Correctly transmitted per Unit of Energy

When I = a PT , the optimum PT that

Maximizes Energy Efficiency will satisfy

~ 1- f (x), f (x) = [1- Q( x )]n, x =rPT

B+ aPT

¶f (x)

¶x=

(B+ aPT )2

rB(PE + PT ). f (x), where x =

rPT

B +aPT

D-

(PT ) =D

(PE + PT ).Teff

= v

f (rPT

B+ aPT

)

(PE + PT )

If Transmitter Knows when Bit is in Error

Energy Consumed Per Correctly Received Bit

0 5 10 15 20 25 300

0.05

0.1

0.15

0.2

0.25

0.3

0.35

γ

D(γ

)

α = 0.9

α = 0.5

α = 0.1

Fig. 4. Optimal transmission power with scaled interference power forvarying levels of interference (α = 0.1, 0.5, 0.9). Data is transmitted inan uncoded fashion using BPSK modulation with packet length n = 100,processing power PE = 2, channel gain r = 1 and noise variance B = 1.

gain to r = 1, with the processing power of the electronic

circuitry set to PE = 2.

IV. TRANSMITTERS WITH CARRIER-SENSING

The previous analysis depends on some key assumptions:

the receiver requests the retransmission of a block or packet

which it deems is in error, the two binary values being

transmitted areequally likely to occur, and the receiver outputs

a zero or one with equal probability when it cannot deter-

mine the value. The last assumption means that the bit error

probability cannot exceed 0.5. There was also the additional

assumption (for a block consisting of n bits) that the bits are

generated at random, and that they are identically distributed

and independent of each other. As a whole these are very

strong assumptions which limit the generality of the results.

In this section we consider a system where error control

that is carried out at the sender using carrier sensing, rather

than at the receiver as in the previous section. It may also

be continuously listening to the noise plus interference even

when it is not transmitting. If the sender transmits a bit and

also listens to the transmission, and “hears” the transmission

plus the noise and interference, its own transmitted signal

will not be attenuated by distance; however the transmitter

can extrapolate the effect of the receiver’s distance in the

signal plus noise and interference. Under the assumption

that the noise plus interference is statistically identical at all

transceivers, the sender then decides whether its transmission

will be correctly received or received with an error, and

retransmits the bit if it considers that a reception error will

occur. Note that this analysis does not assume feedback from

the receiver to the sender at the low level of bits; however, as

in many communication systems, there will be error control

procedures at the receiver (such as HDLC) that request the

retransmission of blocks or packets when parity errors (for

instance) aredetected by thereceiver. In futurework weexpect

to combine the receiver based error control discussed in the

previous section together with the sender’s carrier sensing

discussed in this section.

The system of Figure 1 with the electronic module E and a

transmission unit T still corresponds to the architecture we

consider, and E and T consume power at levels PE , PT

respectively, when a wireless device sends data. If the signal

s ∈ − 1, + 1 is transmitted at power level PT , arriving with

a known attenuation r at the receiver and R =√

rPT , and if

the noise power B plus interference power I measured at the

sender is identical to that at the at receivers as a zero mean

Gaussian random variable V with variance σ2 = B + I , the

probability pe that the sender decides to retransmit the bit is:

pe = Pr ob[V + |R| ≤ 0] + Prob[V − |R| ≥ 0]

= 1−2

σ√

2π

√r PT

0

dxe−x 2

2σ 2

Since the error function is er f (u) = 2√π

u

0e− t 2

dt we write

t = x

σ√

2, u =

√r PT

σ√

2, and:

pe = 1− er frPT

2(B + I )(10)

If as before D is the number of bits to be transmitted, the

effective average number of bits that will be transmitted,

assuming independent errors (but not necessarily independent

bits), is:

Def f =D

er f r PT

2(B + I )

. (11)

If v is the transmission rate in bits per unit time, the energy

consumption for transmitting a bit correctly becomes:

J =PE + PT

v.er f r PT

2(B + I ) )

. (12)

If the interference is created by other similar transceivers

operating at the same transmission power level PT , so that

I = αPT , where α captures the physical characteristics of

the transmission medium, the distances between the different

communicating systems, and the number of communicating

systems which are transmitting at the same time, we have:

Def f (PT ) =D

er f r PT

2(B + αPT )

, (13)

and

J (PT ) =PE + PT

v.er f r PT

2(B + αPT ) )

. (14)

Since er f (0) = 0, and er f (u) ≤ 1 for u > 0 and is monotone

increasing for u ≥ 0, we know that J (PT ) ≥ PE + PT

v. If

B > 0 and PE > 0 then l imPT →0+ J (PT ) = +∞ , and

l imPT →0+ J = +∞ . As a result we have:

Proposition 1 For the set of communicating wireless devices,

if B > 0 and PE > 0, then there is a PoT > 0 that minimises

J (PT ) for PT ≥ 0.

0 5 10 15 20 25 300

0.05

0.1

0.15

0.2

0.25

0.3

0.35

γ

D(γ

)

α = 0.9

α = 0.5

α = 0.1













































rPT , and if





pe = Prob[V + |R| ≤ 0] + Prob[V − |R| ≥ 0]

= 1−2

σ√

2π

√r PT

0

dxe−x 2

2σ 2


u

0e− t 2

dt we write

t = x

σ√

2, u =

√r PT

σ√

2, and:

pe = 1− er frPT

2(B + I )(10)




bits), is:

Def f =D

er f r PT

2(B + I )

. (11)



J =PE + PT

v.er f r PT

2(B + I ) )

. (12)







Def f (PT ) =D

er f r PT

2(B + αPT )

, (13)

and

J (PT ) =PE + PT

v.er f r PT

2(B + αPT ) )

. (14)



v. If






0 5 10 15 20 25 300

0.05

0.1

0.15

0.2

0.25

0.3

0.35

γ

D(γ

)

α = 0.9

α = 0.5

α = 0.1













































rPT , and if





pe = Pr ob[V + |R| ≤ 0] + Prob[V − |R| ≥ 0]

= 1−2

σ√

2π

√r PT

0

dxe−x 2

2σ 2


u

0e− t 2

dt we write

t = x

σ√

2, u =

√r PT

σ√

2, and:

pe = 1− er frPT

2(B + I )(10)




bits), is:

Def f =D

er f r PT

2(B + I )

. (11)



J =PE + PT

v.er f r PT

2(B + I ))

. (12)







Def f (PT ) =D

er f r PT

2(B + αPT )

, (13)

and

J (PT ) =PE + PT

v.er f r PT

2(B + αPT ) )

. (14)



v. If






On Chip Wired Comms Energy per Correctly

Transmitted Bit

A. Simplified piece-wise linear model for pe

Regarding the error function, we know that:

d

dxer f (x) =

2√π

e− x 2

(15)

and its derivative at x = 0 is 2√π

, and decreases as x increases

for x ≥ 0. Since er f (u) ≈ 1 for u ≥ 2, a simple straight-line

approximation sl(u) can be defined as

er f (u) ≈ sl(u) = min 1,u

2, (16)

so that we can write

pe ≈ 1− min 1,rPT

8(B + αPT )(17)

From the previous discussion and (2) we see that:

Def f =D

1− pe

(18)

≈ D i f rPT ≥ 8(B + αPT )

≈ D8(B + αPT )

rPT

otherwise (19)

For a transmission speed which is at v blocks per unit time,

the overall energy consumption per bit that is effectively

transmitted will then be:

J ≈PE + PT

vi f PT ≥

πB

r − πα(20)

PE + PT

v

rPT

π(B + αPT )otherwise (21)

As a consequence:

∂J

∂PT

≈α

v−

BPE

vP2T

(22)

and we readily see that J is minimized if we set the transmis-

sion power to

P ∗T ≈

BPE

α(23)

This simplified analysis provides interesting (but approxi-

mate) observationsregarding theoptimal valueof transmission

power which depends on (a) The power level PE used for

the processing that precedes or accompanies the transmission

itself, as well as on (b) The channel noise power B , and

(c) The constant α which links each of the transmitters’

transmission power to the interference of the transmitters on

each other. The resulting approximate values at the optimum

power operating point are now the block error probability:

p∗e ≈ 1− min 1,1

α + B αPE

, (24)

which is directly related to the effective transmission time per

block:D ∗

ef f

D≈ α +

Bα

PE

, (25)

and finally the total energy consumed per block at theoptimum

operating point is:

J ∗ ≈

√αPE

v[ PE +

B

α][√α +

B

PE

],

≈1

v( αPE +

√B)2. (26)

B. The Case of Wired Systems

Now considered a digital system that includes both compu-

tational and communication units, and suppose that the signal

voltagebeing used for thewired communication module is Vc.

A“box” that communicatesover the wired channels, then hasa

transmission power Pc which isproportional to V 2c , so that we

may write Pc = CV 2c . As before, the computational modules

in the system operate at a power level PE . We assume that

the communication module(s) may use a distinct voltage level

from other devices, and that there is crosstalk or interference

of power level I ≥ 0 as well as noise of power B . Then from

the expression (8), using similar assumptions as before, we

obtain the average energy expended per bit transmitted:

J (Vc) =PE + CV 2

c

v.er f Vcr

2(B + I )

. (27)

1) When crosstalk results from computation and commu-

nication: When both the computation and communication

create interference in the communication system, the crosstalk

will result from both the computation voltage VE so that

PE = bV 2E , and from Pc, so that we may write:

I = αPc + βPE = CαV 2c + bβV 2

E (28)

whereVE is thevoltageused in thecomputational units. Based

on different assumptions one can make, the optimum power

level PcT will differ. In particular, we may assume that the

voltages are the same throughout the system V = Vc = VE

so that I = [Cα + bβ]V 2 and

J (V) = V 2 b+ C

v.er f r C

2( [ B

V 2 + (Cα+ bβ ) ]

. (29)

When all the voltages in the system are the same, if we

can neglect the effect of noise, and the interference is due

to crosstalk, then we see from (27) that we should take the

voltage to be as small as possible. When noise power is non-

zero B > 0, since for V = 0 we have J = +∞ , and similarly

J → +∞ for V → +∞ , we can see that there will be a value

of V , call it V o, that minimizes J .

V. CONCUSIONS

This paper examines the role of power levels in wired and

wireless devices as a means to minimize the overall energy

consumption per unit of data that is effectively transmitted,

in the presence of noise and interference. For wired systems

similar effects arise due to crosstalk that can have the same

effect as interference, causing erors for data being exchanged

between modules in dense semiconductor circuits.



d

dxer f (x) =

2√π

e− x 2

(15)




approximation sl(u) can be defined as

er f (u) ≈ sl(u) = min 1,u

2, (16)



8(B + αPT )(17)


Def f =D

1− pe

(18)


≈ D8(B + αPT )

rPT

otherwise (19)




J ≈PE + PT

vi f PT ≥

πB

r − πα(20)

PE + PT

v

rPT


As a consequence:

∂J

∂PT

≈α

v−

BPE

vP2T

(22)


sion power to

P∗T ≈

BPE

α(23)


mate) observationsregarding theoptimal valueof transmission








p∗e ≈ 1− min 1,1

α + B αPE

, (24)


block:D ∗

ef f

D≈ α +

Bα

PE

, (25)

andfinally thetotal energy consumed per block at theoptimum

operating point is:

J ∗ ≈

√αPE

v[ PE +

B

α][√α +

B

PE

],

≈1

v( αPE +

√B)2. (26)




voltagebeing used for thewired communication module is Vc.

A“box” that communicatesover thewired channels, then hasa

transmission power Pc which isproportional to V2c , so that we





of power level I ≥ 0 as well as noise of power B. Then from



J (Vc) =PE + CV 2

c

v.er f Vcr

2(B + I )

. (27)





PE = bV2E , and from Pc, so that we may write:


E (28)



level PcT will differ. In particular, we may assume that the


so that I = [Cα + bβ]V2 and

J (V) = V 2 b+ C

v.er f r C

2([ B

V 2 + (Cα+ bβ ) ]

. (29)







of V, call it V o, that minimizes J .

V. CONCUSIONS










d

dxer f (x) =

2√π

e− x 2

(15)




approximation sl (u) can be defined as

er f (u) ≈ sl (u) = min 1,u

2, (16)



8(B + αPT )(17)


Def f =D

1− pe

(18)


≈ D8(B + αPT )

rPT

otherwise (19)




J ≈PE + PT

vi f PT ≥

πB

r − πα(20)

PE + PT

v

rPT


As a consequence:

∂J

∂PT

≈α

v−

BPE

vP 2T

(22)


sion power to

P ∗T ≈

BPE

α(23)


mate) observationsregarding the optimal valueof transmission








p∗e ≈ 1− min 1,1

α + B αPE

, (24)


block:D ∗

ef f

D≈ α +

Bα

PE

, (25)

and finally the total energy consumed per block at theoptimum

operating point is:

J ∗ ≈

√αPE

v[ PE +

B

α][√α +

B

PE

],

≈1

v( αPE +

√B )2. (26)




voltage being used for the wired communication module is Vc.

A“box” that communicatesover the wired channels, then hasa

transmission power Pc which is proportional to V 2c , so that we





of power level I ≥ 0 as well as noise of power B . Then from



J (Vc) =PE + CV 2

c

v.er f Vcr

2(B + I )

. (27)





PE = bV 2E , and from Pc, so that we may write:


E (28)



level P cT will differ. In particular, we may assume that the


so that I = [Cα + bβ]V 2 and

J (V ) = V 2 b+ C

v.er f r C2( [ B

V 2 + (Cα+ bβ ) ]

. (29)







of V , call it V o, that minimizes J .

V. CONCUSIONS








How about the Energy for Storage in Queue ??

0 0.5 1 1.5 2 2.5 3 3.5 40.05

0.055

0.06

0.065

0.07

0.075

0.08

0.085

PE

D∗

Fig. 6. Average number of data packets transmitted successfully for eachunit of energy with respect to the processing power PE . We have B = 0.4,r = 1, α = 0.1.

thevoltagesare thesamethroughout thesystem V = Vc = VE

so that I = [αtheta + βb]V 2 and

D (V ) =1

V 2

f r θB

V 2 + αθ+ βb

b+ c. (11)

1) When noise power is negligible (B = 0): When all the

voltages in the system are the same, if we can neglect the

effect of noise, and the interference is due to crosstalk, then

obviously we see from (9) that we should take the voltage to

be as small as possible.

2) When noise power is non-zero (B > 0): In this case,

since for V = 0 we have D ∗ = 0, and similarly D ∗ → 0 for

V → +∞ , we can see that there will be a value of V , call it

V o, that maximizes D ∗ .

VI . EXTENSION TO A TRANSMITTER WITH A FLOW OF

DATA BLOCKS

Typically, a transmitter will receive a flow of blocks of data

from other subsystems in a system such as a mobile device.

These blocksof data may have to be stored in some temporary

location prior to transmission, and the storage will be emptied

of a given data block when the transmitter is assured that the

same block of data has been correctly received at the receiver.

If on the other hand, the receiver signifies to the transmitter

that a particular block contains an error, then the transmitter

will have to retransmit the same block. In some cases, for

instance if a protocol similar to TCP [] is being used, the

transmission rate may have to be adapted to the presence of

errors. Possibly more data blocks than just the one in error

will have to be transmitted again, e.g. the block containing an

error and all of its successors.

In this section we will sketch, but not completely detail

and solve, this extension to our previous analysis. Again, we

consider the most efficient case where only a data block that

contains an error needs to be retransmitted. This is consistent

with the assumption used in Section IV.

We assume that blocks arrive to the processing unit E at a

rateλ according to a Poisson process. The blocksare prepared

for transmission (e.g. encoded) in E in a negligible amount

of time, and then stored as a queue in a memory unit M ,

waiting for transmission and are transmitted in First-Come-

First-Served (FCFS) order. Thedatablock that isat thehead of

the queue is transmitted and retransmitted until it is correctly

received, which means that theeffective transmission timeof a

block, represented by the random variable τ has a distribution

given by Prob[τ = l ] = (1 − p)pl− 1 with mean E[τ ] =

(1− p)− 1 and its variance is Var (τ ) = p(1− p)2 .

We denote by Q(t) the integer valued random process that

represents the number of blocks that are stored at time t ≥ 0.

We will assume that M is efficiently designed so that its

instantaneous power consumption πM is directly proportional

to Q(t), or πM (t) = c.Q(t). From elementary queueing

theory [] we know that the average queue length in steady

state with Poisson arrivals with parameter λ and identically

distributed service times, provided that the system is stable,

i.e. ρ ≡ λ.E [τ ] < 1, is:

E [Q] = l imt→∞ E[Q(t)] (12)

= ρ+ρ2 + λ2Var (τ )

2(1− ρ)

so that the total power consumption of an individual system

becomes:

Π = c[ρ+ρ2 + λ2Var (τ )

2(1− ρ)] + PE + PT (13)

so that the energy consumption per block becomes JB = Π/ λ

or

JB = c[E[τ ] +ρE[τ ] + λVar (τ )

2(1− ρ)] +

PE + PT

λρ (14)

VI I . CONCLUSIONS AND FUTURE WORK

We have studied the energy efficiency in a multi-user com-

munication system when multiple identical transmitter-receiver

pairscommunicatein thesamemedium. Wehaveevaluated the

optimal transmission power that maximizes the average num-

ber of successfully transmitted data packets per unit energy by

taking into account theenergy spent by theprocessing circuitry

aswell as theenergy spent for retransmissions. Wehaveshown

that due to theprocessing energy cost zero-power transmission

over the longest possible duration is not optimal any more,

while increasing the transmission power indefinitely becomes

suboptimal due to the interference caused by simultaneous

transmissions. The optimal transmission power under these

practical system constraints is evaluated numerically, and its

behaviour is identified with respect to system parameters such

as the interference level and the processing power.

The adaptive management of energy systems introduces

additional liabilities and risks, including turning on and off

system components for energy savings that will result in

additional delays [?], and network security issues in the

presence of malicious attacks [?], [?]. These aspects need to

beaddressed in greater detail in futurework. In futureresearch

we also plan to investigate the effect of channel fading and

channel state information on the optimal transmission power

and the system performance.

0 0.5 1 1.5 2 2.5 3 3.5 40.05

0.055

0.06

0.065

0.07

0.075

0.08

0.085

PE

D∗


the voltagesare thesame throughout the system V = Vc = VE


D (V ) =1

V 2

f r θB

V 2 + αθ+ βb

b+ c. (11)











DATA BLOCKS





















rate λ according to a Poisson process. The blocksare prepared








given by Pr ob[τ = l] = (1 − p)pl− 1 with mean E[τ ] =

(1− p)− 1 and its variance is Var (τ ) = p(1− p) 2 .









i.e. ρ ≡ λ.E [τ ] < 1, is:

E [Q] = l imt→∞ E[Q(t)] (12)

= ρ+ρ2 + λ2Var (τ )

2(1− ρ)


becomes:

Π = c[ρ+ρ2 + λ2Var (τ )

2(1− ρ)] + PE + PT (13)


or

JB = c[E [τ ] +ρE[τ ] + λV ar (τ )

2(1− ρ)] +

PE + PT

λρ (14)



munication system when multiple identical transmitter-receiver





aswell as theenergy spent for retransmissions. We haveshown


















0 0.5 1 1.5 2 2.5 3 3.5 40.05

0.055

0.06

0.065

0.07

0.075

0.08

0.085

PE

D∗


thevoltagesare thesame throughout thesystem V = Vc = VE


D (V ) =1

V 2

f r θB

V 2 + αθ+ βb

b+ c. (11)











DATA BLOCKS





















rateλ according to a Poisson process. The blocksare prepared








given by Prob[τ = l ] = (1 − p)pl− 1 with mean E[τ ] =

(1− p)− 1 and its variance is Var (τ ) = p(1− p)2 .









i.e. ρ ≡ λ.E [τ ] < 1, is:

E [Q] = l imt→∞ E[Q(t)] (12)

= ρ+ρ2 + λ2Var (τ )

2(1− ρ)


becomes:

Π = c[ρ+ρ2 + λ2Var (τ )

2(1− ρ)] + PE + PT (13)


or

JB = c[E[τ ] +ρE[τ ] + λVar (τ )

2(1− ρ)] +

PE + PT

λρ (14)



munication system when multipleidentical transmitter-receiver





aswell astheenergy spent for retransmissions. Wehaveshown


















Improvements in Energy Harvesters

Design and characterization of EM energy harvester for

charging rechargeable batteries on time

Life-time of a MicaZ mote can be prolonged

more than 10-times by using energy harvesting

Energy

Harvester

Rectification

and step up

2xAA

Battery

Voltmeter

MicaZ

Mote

A Ampere-

meter

V

Battery Current and Voltage

2.56 Hz2.8 Hz

Vibration characteristics

2.00

2.50

3.00

3.50

4.00

4.50

5.00

5.50

6.00

0 50 100 150 200 250

Buff

er C

apac

itan

ce V

olta

ge (V

)

Time (s)

Labview_VOLT

Received_VOLT

Charging Buffer CapacitanceNode: OFF

Node: Turning ON

Sending data

Node: Turning

OFF

Initiating

Sleep modeBuffer

charging

Running Stop

Energy Harvesting Node 3

0 m

m2

5m

m

25mm

106 Ω1200 T

EM harvester characterized according to wrist vibration

Buck DC-DCRegulated DC

CBuffer

Dickson Rectifier

MicaZ sensor node

Buffer

N

S

Upper cap

Harvester coil

Moving magnet

Fixed magnet

Lower cap

Tube outer boundary

Cylindrical hole

Direction of motion

Tube inner boundary

S

N

Path

Base station

Energy Harvesting Sensor Node +Temperature Sensor

N2 (Walking Node)

N1 (Running Node)

0

5

10

15

20

25

30

3.00

3.50

4.00

4.50

5.00

5.50

0 50 100 150 200 250

TEm

pe

ratu

re (

c)

Bu

ffe

r V

olt

age

(V

)

Time (s)

TEMP_Node2

TEMP_Node_1

TINT_Node_1

VOLT_Node_2

VOLT_Node_1

TINT_Node_2

Energy Harvesting WSN

Charge Management & Regulation

circuitMicaZ Mote

Vreg=2.5v

Vreg

Cbuff

200 µF

Rd1

Rd2

Rh1

Rh2

Vref

VCC

GND

ADCEnergy Harvester

/Rectifier

LTC1540

Buffer Capacitance

Data monitoring

Multimeter

MicaZ Mote

Base station

Piezoelectric & power management circuit

Shaker table

Transmission

Self-Adaptive Energy Harvesting Node

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.00

1.00

2.00

3.00

4.00

5.00

6.00

0 50 100 150 200 250 300 350 400

Acc

eler

atio

n (g

)

Buff

er C

apac

itan

ce v

olta

ge (V

)

Time (s)

ACC

Buf_DAB

Buff_BS

ACC_BS

Self-adaptive MicaZ mote: Quasi-random vibration excitation (Green line) generated through shaker table. Energy status of the buffer measured by Data Acquisition Board (blue line) Measured Data Received through Base-station (red line)

Self-Adaptive Energy Harvesting Node

Designing Online Scheduling Policies

The Energy Packet Network (EPN): Systems Level Discrete Model for Large Scale Systems of

Intermittent Energy Sources and Intermittent Energy Consumers

A Remote Station with Photovoltaic and Wind Energy Operating Security Sensors, a Radar, and Heating/Air-Conditioning

ECROPS – Some Novel Ideas & Results - Discrete Probability Models for Energy-Data Transmission

Optimisation (Energy Packet Networks) – Queues are Batteries and Data Buffers - Holistic Energy Optimisation for the Onboard and Wireless Parts including Interference, Fading, etc. - Design On-Board-On-Chip Real Hardware Harvesters and Optimisers - Develop On-Line Real-Time Decision Algorithms to manage Energy and Data Transmission - Introduce the “Crazy Idea” of Femto-Power Communications with Spins

Successes • 3 ERCs – Haluk Kulah, METU; Deniz Gunduz, Imperial; David Gesbert, Eurecom

• Imperial & CTTC won with European universities and National Instruments, Toshiba Research, Athonet, Worldsensing .. a H2020 Marie Sklodowska-Curie European Training Network on “Sustainable Cellular Networks Harvesting Ambient Energy - SCAVENGE” (2016- 2020)

• Imperial won a UK MoD Grant for ICT Energy Optimisation

• Institutional Links Project Imperial & Sabanci University on “Collaborative Research on Harnessing Renewable Energy Sources for Communications” (UK British Council)

• Other Collaborations: University of Venice Ca` Foscari (Italy), NYU and NJIT (USA)

Publications in Journals (~20) E. Gelenbe, “Synchronising energy harvesting and data packets in a wireless sensor”, Energies, 7, 356-

369, 2014.

S. Chamanian, S. Baghaee, H. Ulusan, O. Zorlu, H. Kulah, and E. Uysal-biyikoglu, “Powering-up Wireless Sensor Nodes Utilizing Rechargeable Battery and Electromagnetic Vibration Energy Harvesting System,” Energies, 7, pp. 6323-6339, 2014.

O. Orhan, D. Gunduz and E. Erkip, Source-channel coding under energy, delay and buffer constraints, IEEE Trans. Wireless Communications, Jul. 2015.

P. Blasco and D. Gunduz, Multi-access communications with energy harvesting: A multi-armed bandit model and the optimality of the myopic policy, IEEE Journal on Selected Areas in Communications, Mar. 2015.

E. Gelenbe, Y. Caseau “The impact of ICT on energy consumption and carbon emissions”, ACM Ubiquity, June 2015.

Publications

Journals (More) R. Gangula, D. Gesbert and D. Gunduz, "Optimization of Energy Harvesting MISO Communication System With Feedback,"

IEEE Journal on Selected Areas in Communications, Mar. 2015 E. Gelenbe “Errors and power when communicating with spins”, IEEE Trans. Emerging Topics in Computing, 3 (4), 483-488,

2015. E. Gelenbe and E. T. Ceran “Energy Packet Networks with Energy Harvesting”, IEEE Access, accepted and online, Feb. 2016. O. Orhan, D. Gunduz and E. Erkip, "Energy harvesting broadband communication systems with processing energy cost,” IEEE

Transactions on Wireless Communications, Nov. 2014 D. Gunduz, K. Stamatiou, N. Michelusi and M. Zorzi, Designing intelligent energy harvesting communication systems, IEEE

Communications Magazine, Jan. 2014. P. Blasco, D. Gunduz and M. Dohler, A learning theoretic approach to energy harvesting communication system

optimization, IEEE Trans. Wireless Communications, Jul. 2013. Numerous Conferences (over 40)

E. Gelenbe, D. Gesbert, D. Gunduz, H. Kulah, E. Uysal- Bıyıkoglu, “Energy Harvesting Communication Networks: Optimization and Demonstration: The E-CROPS Project,” 24th Tyrrhenian Int. Workshop on Digital Comm.:Green ICT, Sep. 23- 25, 2013, Genoa.

M. Shakiba- Herfeh, T. Girici, E. Uysal- Bıyıkoglu, “Routing with Mutual Information Accummulation in Energy Harvesting Wireless Networks,” 24th Tyrrhenian Int. Workshop on Digital Comm.:Green ICT, Sep.23- 25, 2013 .

S. Baghaee, H. Uluşan, S. Chamanian, Ö. Zorlu, H. Külah, and E. Uysal-Biyikoglu, “Towards a Vibration Energy Harvesting WSN Demonstration Testbed,” TIWDC 2013, 24th Tyrrhenian International Workshop on Digital Communications, 23rd-25th Sep. 2013, Genoa.

M. Shakiba-Herfeh and E. Uysal Biyikoglu, “Optimization of Feedback in a MISO Downlink with Energy Harvesting Users,” European Wireless 2014 (EW2014) Barcelona, 14-16 May 2014.

S. Baghaee, H. Ulusan, S. Chamanian, O. Zorlu, H. Kulah, and E. Uysal-Biyikoglu, “Demonstration of Energy-Neutral Operation on a WSN Testbed Using Vibration Energy Harvesting,” European Wireless 2014 (EW2014), Barcelona, Spain, 14-16th May 2014.

http://san.ee.ic.ac.uk

METU - Ankara ECROPS: Minimum Energy with … - 2016.pdfMinimum Energy with Maximum Harvesting for...

Documents

Transcript of METU - Ankara ECROPS: Minimum Energy with … - 2016.pdfMinimum Energy with Maximum Harvesting for...