Efficient Data Communication Protocols for Wireless Networks DISSERTATION DEFENSE Engin Zeydan December 08, 2010 Advisor: Prof. Cristina Comaniciu (Stevens.

DEFENSE 1

Efficient Data Communication Protocols for Wireless

NetworksDISSERTATION DEFENSE

Engin Zeydan

December 08, 2010Advisor: Prof. Cristina Comaniciu(Stevens Institute of Technology)

Co-Advisor: Dr.Didem Kivanc(West Virginia University Institute of Technology)

DEFENSE 2

MAIN CONTRIBUTIONS:

I- Energy-efficient Routing for Correlated Data in Wireless Sensor Networks (WSNs). (PROPOSAL)II- Throughput maximizing Routing for Correlated Data in WSNs.III- Beamforming for multi-user MIMO Ad Hoc Networks.

DEFENSE 3

OUTLINE Introduction for routing in WSNs

System Model & Concepts for WSNs

Game Theory Background

PART II- Throughput Maximizing for Correlated Data in

WSNs

a)Facility Cost Selection for the Congestion Game

b)Simulation Results

PART III- Iterative Beamforming and Power Control

a)Cooperative Algorithm

b)Noncooperative Regret-Matching Algorithm

Conclusions & Future Work

DEFENSE 4

Sink Node

Sensor Node

Efficient distributed routing algorithms are of utmost importance for connectivity and resource allocation of wireless sensor networks (WSNs) . Many routing protocols emphasizing various metrics depending on the application and design specifications.

I. Introduction

DEFENSE 5

Sink Node

A simple game-theoretic model with utility function that account for data correlation for energy minimization and throughput maximization problems.

I. Introduction

DEFENSE 6

Each source node Yi generates a certain amount of data Ψ(Yi), where Ψ(Yi) is the data rate (encoding rate) of source Yi. The units is bits/symbol.

II. System Model

Sink Node

YφN-2

Sensor Node

Y1Yi

YφN

Y2

YφN-1

Relay Node#

# #

source

relay source

DEFENSE 7

The nodes can either send their own raw data directly into the sink, or, they can aggregate.

II. System Model

Sink Node

YφN-2

Sensor Node

Y1Yi

YφN

Y2

YφN-1

Relay Node

DEFENSE 8

Synchronous direct-sequence CDMA (DS-CDMA) where all nodes use a variable spreading sequences of length L.

II. System Model

Sink Node

YφN-2

Sensor Node

Y1Yi

YφN

Y2

YφN-1

Relay Node

DEFENSE 9

The energy per bit Ebi,j for packet transmissions

between nodes Yi and Yj can be defined as:

,

, ( )i j ib

i j c

MPE

mR P

M the packet length, m the information bits in a packet, Pi the constant transmit power for all i, Pc(γ) is the probability of a correct reception, which depends on the achieved SIR, γ. Rij : bit throughput of the link between Yi and Yj

Joule

bits

II. System Model

DEFENSE 10

Rij : bit throughput --> Rij= W/Lij

W : the system bandwidth, Lij : The minimum spreading gain to reach a target

SIR γ*.

*

1, ,, * 2

N

kj kk k i j

i jij i

h P

Lh P

where the link gain hij = 1/dij2,

• dij is the distance of between the nodes Yi and Yj, • σ2 is the thermal noise.

sec

bits

II. System Model

DEFENSE 11

The joint data rate Ψ(Yi, Yj) of two sources Yi and

Yj after data aggregation, is,( , ) max( ( ), ( )) (1 ) min( ( ), ( ))i j i j i j i jY Y Y Y Y Y

II. System Model

Ψ(Yj)

where ρi,j correlation coefficient, and if Gaussian random field data correlation model is used ρ= exp(-d2

Yi,Yj /c)

Ψ(Yi,Yj)

Source Yi

Source YjΨ(Yi)

Data Aggregation at Yj

Correlation constant

0 1

DEFENSE 12

Ψfinal(Ys)

Source Y1 Source Y2

Ψ(Y2)

Ψ(Y1)Data Aggregationat source Ys

. . .

Source Ym

Ψ(Ym)

Ψtemp_1 (Ys)=Ψ (Ys)

ρ=exp(-d2ij/c)

(Ys)

(Ys,Y1)

(Ys,Y2)

Sources Entropy

(Ys,Ym)

Ψtemp_2(Ys)= max (Ψtemp_1 (Ys), Ψ(Y1)) +(1-ρ) min (Ψtemp_1 (Ys), Ψ(Y1))Ψtemp_3(Ys)=

max(Ψtemp_2(Ys), Ψ(Y2))+(1- ρ) min (Ψtemp_2(Ys), Ψ(Y2))

.

.

. Ψfinal (Ys)=max(Ψ(Ym),Ψ(Ytem

p_m (Ys))) + (1- ρ) min (Ψ(Ym),,Ψ(Ytemp_m (Ys)))

Ψtemp_1(Ys)Ψtemp_2(Ys)Ψtemp_3(Ys)

Source Ys

II. System Model

Final Result

Case I: Multiple source Data aggregation Algorithm

DEFENSE 13

II. System Model

Forgetting factor

Ψ(Yi,Yj)YiYj

Data Aggregation

0 1 where

Case II: Multi-hop data aggregation

,

( , ) max( ( ), ( ))

(1 ) min( ( ), ( ))

agg i j agg i agg j

i j agg i agg j

Y Y Y Y

Y Y

Ψ(Yi)=Ψ(Yi)+Ψagg(Yi)

Ψ(Yj)=Ψ(Yj)+Ψagg(Yj)

DEFENSE 14

Sink Node

Yi

, , ( )k l k ls b k k

Joule Joule bitsE E Y

symbol bits symbol

Y2

Y3 Y4Y6

Y7

Y5

SiEb

i,2

Energy per symbol

Y4

Y6

Y5

Ψ(Y4)

Ψ(Y6)

Ψ(Y5)

Energy per Symbol : Eb

2,3Eb

3,4

Eb4,5

Eb6,5

Eb5,7

Eb7,sink

Esi,2

Es2,3

Es3,4

Es4,5

Es6,5

Es5,7

Es7,sink

II. System Model

15

Sink Node

Yi

Λ1,2

Λ2,3

Λ3,4 Λ4,5 R6,

5

Λ5,7 Λ7,sin

k

,

,,

secsec ( )

( )

k l

k lk l k k

k k

bitsR

symbol W

L YbitsY

symbol

Y2

Y3 Y4Y6

Y7

Y5Si

Ri,2

R2,3

R3,4R4,5

Λ6,5

R5,7

R7,sink

Symbol Throughpu

t

Y4

Y6

Y5

Ψ(Y4)

Ψ(Y6)

Ψ(Y5)

Symbol Throughput:

II. System Model

DEFENSE 16

Sink Node

Y1

Sensor Node Y2

Y3 Y4

Y6

Y7

Y5

Bottleneck link

Throughput of Y1 Λ7,sink

Λ1,2

Λ2,3

Λ3,4 Λ4,5

Λ7,sink

Λ6,5

Λ5,7

II. System Model

Λ7,sink

Λ7,sink

Λ7,sink

Λ7,sinkΛ7,sin

kΛ7,sink

S1

Bottleneck Throughput:

DEFENSE 17

Game Theory Background

Finite Strategic Form Games:

1, ,{ }Nm mP A U

the set of players1 2{ , ,..., }NP P P P

1 2{ , ,..., }NA A A A represents the set of actions

1{ } :Nm mU A is the utility function

m ma A is the action of player Pm

1 2( , ,..., ) ( , )N m ma a a a a a action of all players

18

Forms of Equilibrium

Nash Equilibrium

An action profile * * *( , ) max ( , )

m mm m m m m m

a AU a a U a a

*a A is called a pure NE if

Mixed-Strategy Nash EquilibriumA strategy profile

* ( )A is called a mixed-strategy NE

where

( )A is the set of probability space

1 2( , ,..., )N is the joint probability distribution of all players

, m P

* * *

( )( , ) max ( , )

m mm m m m m m

AU U

, m P if

DEFENSE 19

Forms of Equilibrium

Correlated Equilibrium: The probability distribution

( , ) ( , ) ( ' , ) ( , )m m m m

m m m m m m m m m ma A a A

U a a a a U a a a a

( )a is a correlated equilibrium if

Coarse –Correlated Equilibrium

where '

( ) ( ' , )m m

m m m ma A

a a a

( , ) ( , ) ( ' , ) ( )m m

m m m m m m m m m ma A a A

U a a a a U a a a

The probability distribution

( )a is a coarse- correlatedequilibrium if

DEFENSE 20

Classes of Games

Identical Interest Games:The players utilities are same, i.e. for some function

( , ) ( , )m m m m mU a a a a

Potential Games

: A R

An exact potential function Pot(.) is defined as

: , , 'm m mPot A P P a a A

( , ) ( ' , ) ( , ) ( ' , )m m m m m m m m m mu a a u a a Pot a a Pot a a

mP P a A

DEFENSE 21

Classes of Games

Congestion Games:

1 1, ,{ } ,{ } fmNi i f fP F A w

: the set of players1 2{ , ,..., }NP P P P

1 2{ , ,..., }NA A A A represents the set of actions

1{ } :fm

f fw A is the cost of using facility f

{1,2,..., }fF m : the set of facilities

DEFENSE 22

Classes of Games

Congestion Games:

Define

using facility f

( ) { | }f i ma P f a

Then, the utility function is

as the subset of players

( , ) ( ( ))m

m m m f ff a

u a a w a

:mu a

DEFENSE 23

Iterative Updating Schemes

Let T: AA be any mapping from a subset A a=(a1,a2,…,aN) is the set of actions.

Define the updating scheme of actions:a(n+1)=T(a(n)).

The most common updating strategies are: 1-) Jacobi scheme: All components of a=(a1,a2,

…,aN) are updated simultaneously. 2-) Gauss-Seidel scheme: All components of

a=(a1,a2,…,aN) are updated sequentially. 3-) Totally asynchronous scheme: All components

of a=(a1,a2,…,aN) are updated totally asynchronous way.

NR

DEFENSE 24

PART II:

Throughput maximized Routing for Correlated Data in Wireless Sensor

Networks

DEFENSE 25

Motivation:

•Time Critical applications: Deadline (early disaster warning applications or timely detection of events)

•Maintain a certain throughput in order to satisfy the quality-of-service (QoS) requirements and stability requirements under latency constraints in a practical system.

• Trade-off between energy and throughput

DEFENSE 26

Sink Node Senso

r Node

Branch B1

Branch B2

Y1

Yi

YN

Y2

YN-1

YN-2

ΛB1ΛB2

Bottleneck Link Bottleneck

LinkΛB1

ΛB1

ΛB1 ΛB1

ΛB1

ΛB1

Throughput B1:ΛB1nB1

ΛB2

ΛB2

ΛB2ΛB2

ΛB2Throughput B2: ΛB2 nB2

Bottleneck Throughput

Number of sources

Efficient Routing for Throughput Maximization

Branches of a tree:

Si

DEFENSE 27

An NP complete optimization problem!!! A game theoretic formulation Convergence to a local optimal solution with relatively low complexity and in a distributed fashion.

Efficient Routing for Bottleneck Throughput Maximization

Maximize

subject to *,k lSIR , kP C

where ,,

mini

i k lk l B

1

N

ii

i iS X

and iX other possible routes for Yi

DEFENSE 28

Sink Node

Sensor Node Yi

N = {Y1,…….,Yφ}

The congestion game Γ is a tuple (N, F, (Si)iЄN ,(wf) fЄF)

(Si)iЄφF = {1,….,m} (wf) fЄF

(w1)

(w2)(w3)

(w4)

(w5)

Si

Efficient Routing for Throughput Maximization

Relay Node

DEFENSE 29

The utility function for source Yi in our congestion game is:

( , ) ( , )i

i i i f i if S

u S S w S S

where S-i = (S1, S2,………, Si-1, Si+1 ,….,Sφ).

The game performance is influenced by the selection of cost functions wf (Si, S-i) for facilities.

Efficient Routing for Energy Minimization

DEFENSE 30

In setting up the costs for facilities, we can consider several parameters:

Obtained energy or throughput for relaying bits on outgoing route from the facility,

Impact of interference awareness, Opportunity for aggregation by exploiting data

correlation

a) Facility Cost Selection for the Congestion Game

DEFENSE 31

A. Minimum Energy Routing (MER)


Sink Node

Sensor Node

DEFENSE 32

For MER, the following utility function is used

where Ebf is the cost of facility f through the strategy

(or route) Si and S-i.

Source Yi

Facility f1

Ebf1

Facility f2

Ebf2

Strategy Si

Ebf0

( , )i

fi i i b

f S

u S S E


Sink Node


Dr

Interference Aware Routing (IAR) (*)

nf1

nf2

nf3

nf4

nf5

nf6

nf7

nf8

nf9

nf10

nf11

nf12

nf13

Sink Node

Sensor Node

Relay Node

(*) H. Mahmood, C. Comaniciu, Interference aware cooperative routing for wireless ad hoc networks Ad Hoc Networks, vol. 7, no. 1, pp. 248–263, 2009

http://www.scopus.com/scopus/inward/record.url?eid=2-s2.0-53749107681&partnerID=K84CvKBR&rel=3.0.0&md5=3ee0a1fc42f007774e57459edabe4e38

DEFENSE 34


For IAR, the following utility function is used

Source Yi

Facility f1

Ebf1

Facility f2

Ebf2

Strategy Si

i i -iu (S , S ) = -i

ff b

f S

E

nf2nf1

Dr

Ebf0

nf0Sink Node

DEFENSE 35

Maximum Utility

U1U2

U3

U4

U5

Throughput Maximizing Correlation Aware Routing (T-CAR)

Sink Node

Sensor Node


DIRECT

DEFENSE 36

Throughput Maximizing Correlation Aware Routing (T-CAR)

Sink Node

Sensor Node


T-CAR

DEFENSE 37

Utility Function of source Yi forT-CAR:

D,Sink Node

Sensor Node

Y1

Yi

YN

ΛB1

New Bottleneck Link

Bottleneck Throughput

Prune sub-tree

of Yi 1 1 1 1( , ) ( ) '

ii i i B B B Y Bu S S n n n

Λ'B1

1 11 B Bu n

nYi

Number of sources at subtree Yi

Branch B1


1 2( , )i i iu S S u u

1 12 ( ) 'iB Y Bu n n ( )NY1( )NY

2( )Y

1( )i Y

1( )Y

( )iY

Y2

YN-1

1

1, 1( )BD

W

L Y

1

1, 1

'( )B i

D

W

L Y Si

DEFENSE 38

A Potential Game Formulation for T-CAR


It can be shown that T-CAR is an exact potential game with the potential function,

1

( , )N

i i ii

P S S

1 1 1 1( , ) ( ) '


Therefore, T-CAR converges!

DEFENSE 39

Difference from T-CAR is starting tree:

T-ICAR starting tree IART-CAR starting tree MER or DIRECT

Throughput maximizing interference and Correlation Aware Routing (T-ICAR)

The utility of source Yi:


1 1 1 1( , ) ( ) '


DEFENSE 40

Proposition 1: Let Sdirect be the selected strategy for each source Yi, ∀ i ∈ N where all nodes communicate directly with sink node. Then, the set of state Sdirect = {S1,S2, ..., Sφ} is NE solution

Condition for the Nash equilibrium (NE) strategy

where Li,D is the minimum spreading gain from node Yi to sink D,Li,j is the minimum spreading gain between nodes Yi and Yj.

,i j

i j

Y Y N

Y Y

,, ,

, ,

2

( )j D

i j i ji D j D

L

L L

, , (2 )i j j D ijL L

elseif

if

, , (2 )i j j D ijL L ,

, ,, ,

2

( )j D

i j i ji D j D

L

L L

and

and

DEFENSE 41

Proof of Proposition 1:

Yi

D

Yj

Yi

D

Yj

DIRECT

,

( , )i i ii D

Wu S S

L , ,

,

2( ' , )

( (1 ) )i i ij D i j

j D

Wu S S

L

W

L

S’iSi

Ψ(Yi) = Ψ(Yj) = μ (bits/symbol)

Bottleneck link

1-)

CASE 1:

DEFENSE 42


Yi

D

Yj

Yi

D

Yj

DIRECT

S’iSi

, , ,(2 )i j j D i j

W W

L L

Bottleneck link

, , ,(2 )i j j D i jL L 2-)

CASE 1:

DEFENSE 43


Yi

D

Yj

Yi

D

Yj

DIRECT

SiS’i

,i j i jY Y N Y Y ,

, ,, ,

2

( )j D

i j i ji D j D

L

L L

Therefore, if , , ,(2 )i j j D i jL L

and

Bottleneck link

CASE 1:

DEFENSE 44


Yi

D

Yj

Yi

D

Yj

DIRECT

,

( , )i i ii D

Wu S S

L , ,

2( ' , )i i i

i j j D

W Wu S S

L L

S’iSi

Ψ(Yi) = Ψ(Yj) = μ (bits/symbol)

Bottleneck link

1-)

CASE 2:

DEFENSE 45


Yi

D

Yj

Yi

D

Yj

DIRECT

S’iSi

, , ,(2 )j D i j i j

W W

L L

, , ,(2 )i j j D i jL L 2-)

Bottleneck link

CASE 2:

DEFENSE 46


Yi

D

Yj

Yi

D

Yj

DIRECT

SiS’i

,i j i jY Y N Y Y

,, ,

, ,

2

( )j D

i j i ji D j D

L

L L

Therefore, if , , ,(2 )i j j D i jL L

and

Bottleneck link

CASE 2:

DEFENSE 47

Corollary: For a special case when

Condition for the Nash equilibrium strategy

Then, Sdirect is a NE point.

2,

, exp( )i ji j

d

c

2,

,

1log( )

i j

i j

dc

,i j

i j

Y Y N

Y Y

, , (2 )i j j D ijL L

elseif

if

, , (2 )i j j D ijL L

2,

,

1log( )

i j

i j

dc

DEFENSE 48

Condition for the Nash equilibrium strategy

Corollary 2: For a special case when c=0 (no correlation), and

state Sdirect is a NE point

, ,2i j j DL L , ,i j i jY Y N Y Y

DEFENSE 49

The number of nodes in the network is selected to be N = 4 to 40, uniformly distributed over a square area of dimension 100m X 100m.

The target SINR is selected to be γ*= 5 (7 dB) Constant transmit Power Pi =10-2 Watts (10 dBm),

σ2= 10-13 Watts, W=1 Mhz, forgetting factor=0.8. Each symbol is represented with 1 bits, i.e.

Ψ(Yi)=1bits/symbol for all Yi. The spatial correlation of data is chosen to be

c=0 (no aggregation), c = 100 (low correlated) and c=1000 (highly correlated). ρij=exp(-d2

ij/c).

b) Simulation Results

DEFENSE 50

Start TCAR with MER when φ=0.5 (half relay nodes, half source nodes) and with DIRECT when φ=1.0 (all source nodes)

T-ICAR always starts with IAR. Use Dr=16m, for the best performance of IAR

(Trade-off between energy and throughput). MER and IAR perform data aggregation

opportunistically based on the routes set-up, i.e. whenever the routes meet

Average over 1000 different topologies


DEFENSE 51


(a) MER (b) IAR

N=24, φ=0.5 (half source, half relay), and c=100, Dr =16m

0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

60

70

80

90

100

Relay

SourceSink

0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

60

70

80

90

100

Relay

Source

Sink

DEFENSE 52


(c) T-CAR (d) T-ICAR


0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

60

70

80

90

100

Relay

Source

Sink

0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

60

70

80

90

100

Relay

Source

Sink

DEFENSE 53


10 15 20 25 30 35 40150

200

250

300

350

400

Number of nodes (N)

Tota

l th

roughput

(kbps)

T-CAR

DIRECT

MER

T-CAR throughput improvements MER DIRECT

• N=10 (72 %) (16 %) • N=40 (70 %) (54 %)

70 %

φ=1 (all sources), and c=1000.

DEFENSE 54


10 15 20 25 30 35 4010

-3

10-2

10-1

100

101

Number of nodes (N)

Tota

l energ

y (

Joule

/bits)

DIRECT

T-CAR

MER

TCAR Energy loss MER• N=10 (81 %) • N=40 (55 %)

φ=1 (all sources), and c=1000.

55 %

81 %

DEFENSE 55

b) Simulation ResultsN=24, φ=0.5 (half source, half relay), and c=100, Dr =16m

IAR Throguhtput Improvements MER

8.23 %

8.23 %

1 2 3 4 5 6 7 890

100

110

120

130

140

150

160

170

180

Number of iteration

Tot

al t

hrou

ghpu

t (k

bps)

T-ICAR

T-CARIAR

MER

DEFENSE 56


Throguhtput improvements T-ICAR T-CAR IAR MER

4.36% 70% 84%

84 %


1 2 3 4 5 6 7 890

100

110

120

130

140

150

160

170

180

Number of iteration

Tota

l th

roughput

(kbp

s)

T-ICAR

T-CARIAR

MER

DEFENSE 57


Energy Loss of IAR MER 9.09 %

9 %


1 2 3 4 5 6 7 810

-3

10-2

10-1

100

Number of iteration

Tot

al e

nerg

y (J

oule

/bits

)

T-ICAR

T-CAR

IAR

MER

DEFENSE 58


Energy Loss of T-ICAR & TCAR IAR MER 97.06%

97.32%

97 %


1 2 3 4 5 6 7 810

-3

10-2

10-1

100

Number of iteration

Tot

al e

nerg

y (J

oule

/bits

)

T-ICAR

T-CAR

IAR

MER

DEFENSE 59


0 100 200 300 400 500 600 700 800 900 100050

100

150

200

250

300

350

Correlation constant (c)

Tot

al t

hrou

ghpu

t (k

bps)

TCAR (N=20)

TCAR (N=10)MER (N=10)

MER (N=20)

TCAR improvements over MER c=200 c=800

• N=10 (51.30 %) (43.24 %)

• N=20 (56.38 %) (46.52 %)

φ=1All sources

56%

46%

DEFENSE 60


1 2 3 4 5 6 7 8 9 10 11 12 13 14 151

1.1

1.2

1.3

1.4

1.5

1.6

1.7

Number of iterations

Nor

mal

ized

thr

ough

put

N=40

N=30N=20

N=10

TCAR improvements over DIRECT (TCAR/DIRECT)

61


Comparisons with Optimal Throughput Maximizing Routing (search over 125 different trees) for N+1=5, φ=1, and c=1000

OPT TCAR MER DIRECT

Throughput (kbps)

311.6 303.26 236.47 280.03

Energy (nJ/bits)

3.0 3.4 0.6 5.3

97 %

76 %

80 %82 %Loss

DEFENSE

DEFENSE 62

The problem of efficient transmission structure in WSNs to minimize the total energy and to maximize throughput.

The impact of correlation structure in establishing routing paths towards the sink.

Distributed iterative protocols based on a game theoretic framework which are shown to converge within a couple of iterations.

Significant energy reductions and throughput gains over classic approaches can be achieved.

c) Conclusions

DEFENSE 63

c) Future Work1) Similar design approach can be used for: Rate Distortion using multi-hop routing., Network lifetime maximization., end-to-end delay minimization

through mutual information accumulation, data accuracy,

latency, data security, capacity, etc…2) Aggregation Cost can also be incorporated into utility function easily,3) Pareto optimal tree configuration, 4) Applying adaptive learning algorithms (Regret Matching, Simulated Annealing, Genetic Algorithms,

etc.)5) Comparison with Cluster-based approaches

DEFENSE 64

PART III:

Joint Iterative Beamforming and Power Adaptation for MIMO Ad-hoc

Networks

DEFENSE 65

Introduction

Interference management by performing a joint iterative transmit beamforming and power adaptaion in a multi-user MIMO ad hoc network.

Objective: Minimize the total transmit power in the network considering the interference from other nodes in the network.

“Transmit beamformers” are selected from a “predefined codebook” known for both Tx’s and Rx’s for multi-user MIMO networks.

The nodes optimize their performance by modifying their beamform patterns and powers

Grassmanian subspace packing codebook generation,[*]

1

2

1

( )

( )

.

.

( )

k

k

k

k T Tx

t

t

t

t

Codeword

where Tkt

21kt

Goal: Maximize SNR and therefore minimize BER!

T: number of antennas

1 2{ , ,..., }k k kt t t

Codebook

size γ

(*) Love, D.J., Heath Jr., R.W. , Strohmer, T. “Grassmannian beamforming for multiple-input multiple-output wireless systems “ IEEE Transactions on Information Theory, 2003

http://www.scopus.com/scopus/inward/record.url?eid=2-s2.0-0242334025&partnerID=K84CvKBR&rel=3.0.0&md5=8c19592e47bbd46c4d294e98d2230a19





DEFENSE 67

Grassmanian subspace packing codebook generation (*)

T: 2, γ=4

-0.1612 - 0.7348i -0.0787 - 0.3192i -0.2399 + 0.5985i -0.9541, , ,

-0.5135 - 0.4128i -0.2506 + 0.9106i -0.7641 - 0.0212i 0.2996

0.7939 + 0.0590i 0.2189 + 0.0654i 0.3087 - 0.4341i 0.5915 - 0.1175i

-0.4126 - 0.0807i , 0.1844 - 0.3191i , -0.2454 - 0.6507i , 0

-0.0853 - 0.4269i -0.8804 - 0.1921i 0.4817 + 0.0258i

.3113 + 0.6635i

0.2941 + 0.1128i

T: 3, γ=4

(*) http://cobweb.ecn.purdue.edu/~djlove/grass.html

DEFENSE 68

Codeword selection in Single User Scenario

, ,arg max( )k

H Hk k k k k k k

tt t H H t

0

, ,k H H

k k k k k k

Pt H H t

0 : Target SNR

DEFENSE 69

Choose Tx beamformer with minimum Power

Rx 1Tx 1 Rx 2Tx 2

Rx kTx kRx NTx N

User 1

User k User N

User 2

1 1( , )P t 2 2( , )P t

( , )k kP t ( , )N NP t

0 : Target SINR

Interference

DEFENSE 70

Multi-User Case

Node pair m

Tx

Rx

, ,m m m m m m i m i i i mi m

r P H t b PH t b n

Signal Interference

+Noise

1 2{ , ,..., },m m mm mt t t t Transmit

Beamformer

1,

1,

,|| ||

m m m mm

m m m m

R H tw

R H t

Normalized Receive Beamformer

2|| || 1mw

Multi-user Interferenc

e

2, ,( , ) H H

m m m i m i i i m ii m

R P PH t t H I

Interference+Noise Covariance Matrix

1 2 1 2[ , ,..., ], [ , ,..., ]N Nt t t P P P P Define

( , )m mP t

2|| || 1mt

DEFENSE 71

Multi-User Case

2, 1

, ,2 2,

| |

| |

Hm m m m m H H

m m m m m m m m mHi m m i i

i m

P w H tP t H R H t

P w H t

Received signal-to-interference plus noise ratio (SINR)

01

, ,m H H

m m m m m m m

Pt H R H t

Power can also be adjusted based on received normalized SINR

arg maxm m

optm m

tt

Receiver Selects the best index of transmit beamformer:

Limited-Rate Feedback: (Extension to Multi-user case)

Convergence is not guaranteed!

DEFENSE 72

Optimization Problem

Minimize 1

N

mm

P

|| || || || 1m mw t

subject to 0m

min max ,mP P P {1,2,..., }m N

,m mt

,P

DEFENSE 73

Game Theory Interpretation

: the set of players (node pairs)

The game

1, ,{ }Nm mN C U

{1,2,..., }N N

1 2{ , ,..., }NC C C C : represents the set of actions (transmit beamformer and powers)

1{ } :Nm mU C : the utility function

min max[ , ]mP P PActions are:1 2{ , ,..., }m m mm mt t t t

mc C

DEFENSE 74

Centralized SolutionMinimize

* *

, 1

( , ) arg min ( , )N

m mP m

P P P

* * * * * * * *

1 2 1 2[ , ,..., ], [ , ,..., ]N Nt t t P P P P

where0

1, ,

( , )m m H Hm m m m m m m

P Pt H R H t

Note that * * * *1 2[ , ,..., ]Nt t t * * * *

1 2[ , ,..., ]NP P P Pgives

DEFENSE 75

Maximize

1

( , ) ( , )N

network m mm

U P P P

Identical Interest Game: All users utilities are same.

Cooperative Power Minimization Algorithm (COPMA)

1

( , ) ( , )N

m network m mm

U U P P P m N

DEFENSE 76


Node pair m

Node pair n

Node pair l

Node pair k

• Initialize with index one for transmit beamformers and maximum powers for all node pairs 1

m m mt t

maxmP P

1n n nt t

maxnP P

1k k kt t

maxkP P1

l l lt t

maxlP P

DEFENSE 77


Node pair m

1currentm mt t

maxcurrentmP P

updatedm mt updated

mP

Node pair n

Node pair l

Node pair k

[ , , ]current updatedm mm P P

[ , , ]current updatedn nn P P

[ , , ]current updatedk kk P P

[ , , ]current updatedl ll P P

Randomly choose

DEFENSE 78


Node pair m

Node pair n

Node pair l

Node pair k

Calculate1

Nupdated

updated mm

P P

Calculate1

Ncurrent

current mm

P P

DEFENSE 79


Node pair m

Node pair n

Node pair l

Node pair k

1Pr( )

1 exp(( ) / )updated currentP P

Keep with probabilityupdatedmt Smoothing

factor ~ 1/n2

DEFENSE 80


Node pair m

Node pair n

Node pair l

Node pair k

current updatedm mP P m N

If is keptupdatedmt

else no change ! (don’t update)

DEFENSE 81


Node pair m

1currentn nt t current

nPupdatedm mt updated

mPNode pair n

Node pair l

Node pair k

[ , , ]current updatedm mm P P

[ , , ]current updatedn nn P P

[ , , ]current updatedk kk P P

[ , , ]current updatedl ll P P

Randomly choose

DEFENSE 82


Node pair m

Node pair n

Node pair l

Node pair k

Calculate1

Nupdated

updated ii

P P

Calculate1

Ncurrent

current ii

P P

DEFENSE 83


Node pair m

Node pair n

Node pair l

Node pair k

1Pr( )


Keep with probabilityupdatednt

DEFENSE 84


Node pair m

Node pair n

Node pair l

Node pair k

current updatedn nP P n N

If is keptupdatednt

else no change ! (don’t update)

DEFENSE 85


Node pair m

Node pair n

Node pair l

Node pair k

DEFENSE 86


Inititalization: The initial index of transmit beamformer is one and initial transmit power is maximum for all node pairsRepeat: Sequentially choose a node pair m. Denote tm(n) as the current transmit beamformer at iteration n for the m’th node pair.

Until: Predefined number of iterations

1-) Set tm(n)=tm(n-1).

1

Ncurrent

current ii

P P

2-) Randomly choose a transmit beamformer and calculate

1

Nupdated

updated ii

P P

updatedm mt

3-) Keep with probabilityupdatedmt

1


and

DEFENSE 87

Theorem: COPMA converges to optimal profile

with arbitrarily high probability. In other words,


* * * *1 2[ , ,..., ]Nt t t

Proof: Based on Markov chain analysis

* *

0lim lim ( ( ) ) 1

kP k

is the transmit beamformer profile at iteration k

1 2( ) [ ( ), ( ),..., ( )]Nk t k t k t k where

DEFENSE 88

11 12 1 j 1

21 22 2 j 2

1i 2i ij i

1 2 j

Two Players Markov Chain

1 111 1 2[ , ]t t 1 1

11 1 2( ) [ , ]P P P

Optimal

DEFENSE 89

11 12 1 j 1

21 22 2 j 2

1i 2i ij i

1 2 j

Two Players Markov Chain

12 11Pr ( | ) 1 11Pr ( | )

DEFENSE 90

* * * *11 1 11 1 11 1

2 2

Pr ( ) Pr ( | ) Pr ( ) Pr ( | )p p pp p


The stationary distribution is calculated from

~2

*~

( )

exp( ( ( )) / )Pr ( ( ))

exp( ( ( )) / )k

P kk

P k

Then

1 111 11

1Pr ( | )

2 (1 exp(( ( ) ( )) / ))ppP P

* *

0lim lim Pr ( ( ) ) 1

kk

and

*Pr (.)

DEFENSE 91

Non-Cooperative Power Control : For non-cooperative selection, convergence of transmit beamformer is problematic under constant SINR requirements!• Noncooperative beamforming for multi-user MIMO ad-hoc networks lacks the quality of “strategic complementarities” that are found in power control-only games.• If a node pair adjusts its transmit beamformer to increase its own received SINR, this change may either increase or decrease the received SINR of every other node pair

Noncooperative beamforming and Power Control

Regret Matching based Selection Game (RMSG)

1 1( 1) ( ) ( ( , ( )) ( ( ), ( ))m mt t

m m m m m m m m

kR k R k U t t i U t i t i

k k

1

1

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

1m

ktm m m m m m m

i

R k U t t i U t i t ik

• We study a non-cooperative learning algorithm called the regret matching adaptive algorithm from (*), in which the players choose their actions based on the regret for not choosing particular actions in the past. 1 2[ , ,..., ]m m m mt t t tDenote

as the vector of all strategies

Define the average regret vector for an action vectormt

Update the average regret vector based on formula:

(*) S. Hart and A. Mas-Colell, “A simple adaptive procedure leading to correlated equilibrium,” Econometrica, vol. 68, no. 5, pp. 1127–1150, 2000

DEFENSE 93


[ ( )]( ) Pr ( ( ) )

[ ( )]

m

m

m

m m

tt mm m m t

mt

R kk ob t k t

R k

1, ,( , ( )) log( ( , ) )H H

m m m m m m m m m m m mU t t k t H R P H t

• Choose an action according to probability distribution:

• The utility function for noncooperative users is:

• Local information

DEFENSE 94

Inititalization: The initial index of transmit beamformer are chosen randomly and initial transmit power is maximum for all node pairs

For k=1,….,ITER


For m=1,….,N1) Calculate

1 1( 1) ( ) ( ( , ( )) ( ( ), ( ))m mt t

m m m m m m m m

kR k R k U t t i U t i t i

k k

2) Update the probability distribution[ ( )]

( ) Pr ( ( ) )[ ( )]

m

m

m

m m

tt mm m m t

mt

R kk ob t k t

R k

Next mNext k

3) Updatemt0

1, ,( , )m H H

m m m m m m m m m

Pt H R P H t


Facts: 1-) Every finite strategy game has a mixed strategy Nash equilibrium.2-) For all finite games, using a proper learning algorithm, the game can be shown to converge to the fixed points of probability. 3-)The advantage of regret matching- based selection is that it is distributed and requires limited information exchange4-) The time-averaged behavior of regret-matching game converges almost surely (with probabilityone) to the set of coarse-correlated equilibrium (*)

(*) H. P. Young, “Strategic learning and its limits,” in Oxford University Press, 2005.

DEFENSE 96

The number of node pairs in the network is selected to be N = 4 (small network) , uniformly distributed over a square area of dimension 30m X 30m and N=10 (large network), uniformly distributed over a square area of dimension 100m X 100m.

The target SINR is selected to be γ*= 10 dB. Transmit Power range Pi = [1mW, 5mW, 20mW,

30mW, 50 mW, 100mW ], σ2= -95 dBm. Each entry in the channel matrix is i.i.d. Gaussian

random variables and don’t vary throughout iterations.

For each node pair, codebook size is ϒ=16 and number of antennas is T=3.


DEFENSE 97

10 20 30 40 50 60 70 80 90 100 110 12010

-2

10-1

100

Iteration

To

tal t

ran

smit

Po

we

r (W

)

RMSG

COPMACentralized

Simulation Results

68 %

N=4 (Small Network), τ=0.1/k2 ,

52 % Close to optimal

DEFENSE 98

Simulation Results

0 20 40 60 80 100 1200

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

Iteration

Tra

nsm

it P

ow

ers

(W

)

User 1

User 2User 3

User 4

COPMA Transmit Power

DEFENSE 99

Simulation Results

0 20 40 60 80 100 1200

2

4

6

8

10

12

14

16

Iteration

Tra

nsm

it B

ea

mfo

rme

r In

de

x

User 1

User 2

User 3

User 4

COPMA Transmit Beamformer Index

DEFENSE 100

Simulation ResultsRegret-Matching probability mass function (p.m.f)

0 5 10 15 200

0.02

0.04

0.06

0.08Iteration 1

Index Value

P.m

.f

0 5 10 15 200

0.1

0.2

0.3

0.4Iteration 12

P.m

.f

Index Value

0 5 10 15 200

0.2

0.4

0.6

0.8Iteration 50

P.m

.f

Index Value0 5 10 15 20

0

0.5

1Iteration 100

P.m

.f.

Index Value

DEFENSE 101

Simulation Results

0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

60

70

80

90

100

Receiver

Transmitter

COPMA

N=10(Large Network), TRANSMIT BEAMPATTERNS

DEFENSE 102

Simulation Results

76 %

200 400 600 800 1000 1200 14000

0.1

0.2

0.3

0.4

0.5

Iteration

To

tal t

ran

smit

Po

we

r (W

)

RMSG

COPMA

N=10(Large Network), τ=200/k2 ,

Close

DEFENSE 103

Simulation ResultsN=10, Probability mass function, RMSG

0 5 10 15 200

0.02

0.04

0.06

0.08Iteration 1

Index Value

P.m

.f

0 5 10 15 200

0.1

0.2

0.3

0.4Iteration 500

P.m

.f

Index Value

0 5 10 15 200

0.2

0.4

0.6

0.8Iteration 1000

P.m

.f

Index Value0 5 10 15 20

0

0.5

1Iteration 1500

P.m

.f.

Index Value

DEFENSE 104

Conclusion Joint Beamforming (Codebook selection) and

Power Control in multi-user Wireless Ad-hoc Networks.

Cooperative Power Control : Choose Tx beamform randomly and keep the current one with high probability if it gives lower total network power.

Non-Cooperative Power Control : For non-cooperative selection, convergence of transmit beamformer is problematic!

Learning : Regret-matching based learning is used to for probabilistic convergence.

The selection is performed based on ‘’regret’’.

DEFENSE 105

FUTURE WORK Better Codebook: Codebook adaptation using

evolutionary learning (Genetic Algorithms, etc.) Modifying regret-matching for convergence to

NE or Pareto Optimal point for regret matching techniques

Apply same learning strategies to other joint transmission adaptation parameters (joint CDMA waverform design and power adaptation, channel selection and continous beamforming update, rate and modulation adaptations, etc. )

DEFENSE 106

PUBLICATIONS (*)

(*) http://www.ece.stevens-tech.edu/~ezeydan/

•E. Zeydan D. Kivanc and U. Tureli, “Iterative Beamforming and Power Control for MIMO Ad Hoc Networks” in Proc of IEEE GLOBECOM'10, Miami, FL, Dec. 2010.

•E. Zeydan D. Kivanc, C. Comaniciu and U. Tureli, “Bottleneck Throughput Maximization for Correlated Data Routing: A Game Theoretic Approach” in Proc. of CISS'10, Princeton, NJ, March 2010.

•E. Zeydan D. Kivanc and C. Comaniciu, “Efficient Routing for Correlated Data in Wireless Sensor Networks” in Proc of IEEE MILCOM’’08, San Diego, CA, Nov. 2008.

•E. Zeydan, D. Kivanc and U. Tureli, “Cross Layer Interference Mitigation using a convergent Two-Stage Game for Ad Hoc Networks” in Proc. of CISS'08, Princeton, NJ, March 2008.

•E. Zeydan D. Kivanc and U. Tureli, “Unitary and Nonunitary Differential Space Frequency coded OFDM” in Proc of IEEE Wireless Communications and Networking Conference (WCNC'08), Las Vegas, NV, April, 2008.

•E. Zeydan, D. Kivanc and U. Tureli, “Joint Iterative Channel Allocation and Beamforming Algorithm for Interference Avoidance in Multiple-Antenna Ad Hoc Networks” in Proc. of 2007 IEEE MILCOM, Orlando, FL, Oct. 2007.

•E. Zeydan, U. Tureli "Differential Space-Frequency Group Codes for MIMO-OFDM " in Proc. of 41st Annual Conference on Information Sciences and Systems (CISS'07), Baltimore, MD, March 2007.

http://www.ece.stevens-tech.edu/~ezeydan/pdf/GLOBECOM_2010.pdf



http://www.ece.stevens-tech.edu/~ezeydan/pdf/CISS_2010.pdf

http://www.ece.stevens-tech.edu/~ezeydan/pdf/CISS_2010.pdf

http://www.ece.stevens-tech.edu/~ezeydan/pdf/Milcom'08.pdf

http://www.ece.stevens-tech.edu/~ezeydan/pdf/CISS'08.pdf


http://www.ece.stevens-tech.edu/~ezeydan/pdf/WCNC'08.pdf







DEFENSE 107

Thank You !

Questions, Comments !

DEFENSE 108

DEFENSE 109

PART I:

Energy Efficient Routing for Correlated Data in Wireless Sensor

Networks

DEFENSE 110

Minimize

subject to *,k lSIR , kP C

An NP complete optimization problem!!! A game theoretic formulation Convergence to a local optimal solution with relatively low complexity and in a distributed fashion.

Efficient Routing for Energy Minimization

1

( )N

kb k k

k

E Y

i iS X

where iX other possible routes for node Yi

DEFENSE 111

In setting up the costs for facilities, we can consider the following parameters:

Energy spent for relaying bits on outgoing links from the facility,

Opportunity for aggregation by exploiting the data correlation


DEFENSE 112

Maximum Utility

MER

U1U2

U3

U4

U5

B. Correlation Aware Routing (CAR)

Sink Node

Sensor Node


DEFENSE 113

CAR

Sink Node

Sensor Node


DEFENSE 114

Utility Function of source Yi for CAR:

Sink Node

Sensor Node

Y1

Yi

YN

Prune sub-tree

of Yi ( , ) - ( ) ( )i

f ii i i b f f f f

f S

u S S E Y Y

1 - ( )i

fb f f

f S

u E Y


1 2( , )i i iu S S u u

2 - ( )i

f ib f f

f S

u E Y

Si

( )NY

YN-1

1( )NY

Y2

2( )Y

( )iY

1( )Y 1( )i Y

DEFENSE 115

A Potential Game Formulation for CAR

An exact potential function P(.) is defined as: , , 'i iP S R i N S S S

( , ) ( ' , ) ( , ) ( ' , )i i i i i i i i i iu S S u S S P S S P S S

A best response strategy in a potential game converges to a Nash equilibrium.


It can be shown that CAR is an exact potential game with the potential function,

1

( , )N

ii i s

i

P S S E

Therefore, CAR converges!

( , ) - ( ) ( )i

f ii i i b f f f f

f S

u S S E Y Y

DEFENSE 116

Minimum Energy Data Gathering Algorithm (MEGA) [Rickenbach et. al .DIALM-POMC’04]


Yj

Yi

YN ,,( , ) - ( ) (1 ) ( )

j

i j fi i i b i i i j i i b

f M

u S S E Y Y E

MiMinimum Energy

route

Ci

Coding route

( )i iY

,(1 ) ( )i m m mY

Ym

Coding routeCi

MER route of Yj

Sink Node

Coding routeMER route

DEFENSE 117

The number of nodes in the network is selected to be N = 10 to 40, uniformly distributed over a square area of dimension 40m X 40m.

The target SINR is selected to be γ*= 5 (7 dB)

Constant transmit Power Pi =10-2 Watts (10 dBm), σ2= 10-13 Watts, W=1 Mhz, forgetting factor=0.8.

Each symbol is represented with 1 bits, i.e. Ψ(Yi)=1bits/symbol for all Yi.

MER constructs route and aggregates data opportunistically.


DEFENSE 118

The spatial correlation of data is chosen to be c=0 (no aggregation), c = 100 (low correlated) and c=1000 (highly correlated). ρij=exp(-d2

ij/c). To compare CAR, MER and MEGA fairly, total

energy required for a total symbol throughput of 100 kbps is compared. (“effective energy”)

φ=1 (all sources, no relays!) Average over 100 different topologies.


DEFENSE 119


(a) MER (b) CAR

N=30, c=1000

0 5 10 15 20 25 30 350

5

10

15

20

25

30

35

40

Source

Sink

(c) MEGA

0 5 10 15 20 25 30 350

5

10

15

20

25

30

35

40

Source

Sink

0 5 10 15 20 25 30 350

5

10

15

20

25

30

35

40

Source

Sink

DEFENSE 120

c=100 improvement of CAR compared to MER MEGA

N=10 (4.31 %) (14.30 %)

N=40 (25.35 %) (52.18 %)


10 15 20 25 30 35 4010

-3

10-2

10-1

100

Number of Nodes (N)

Tot

al E

ffec

tive

Ene

rgy

(Jou

le/s

ymbo

l)

MER, CAR, MEGA (c=0)MEGA (c=100)

MER (c=100)

CAR (c=100)

MEGA (c=1000)

MER (c=1000)CAR (c=1000)

52 %25 %

c=100

c=1000

c=0

DEFENSE 121

c=0 (no aggregation) improvements of CAR

@ c=100 (93.15 %)

@ c=1000 (96.29 %)


10 15 20 25 30 35 4010

-3

10-2

10-1

100

Number of Nodes (N)

Tot

al E

ffec

tive

Ene

rgy

(Jou

le/s

ymbo

l)

MER, CAR, MEGA (c=0)MEGA (c=100)

MER (c=100)

CAR (c=100)

MEGA (c=1000)

MER (c=1000)CAR (c=1000)

96 %

c=0 (no aggregation)

DEFENSE 122

CAR improvements (N=20) compared to MER MEGA • c=200 (16.73 %)

(31.46%)• c=800 (16.36 %) (16.61

%)


0 100 200 300 400 500 600 700 800 900 1000

10-3

10-2

Correlation Constant (c)

Tota

l E

ffective E

nerg

y (

Joule

/sym

bol)

MEGA (N=20)

MER (N=20)

CAR (N=20)MEGA (N=10)

MER (N=10)

CAR (N=10)

16 %

31 %

DEFENSE 123


1 2 3 4 5 60.75

0.8

0.85

0.9

0.95

1

Number of Iterations

Nor

mal

ized

Eff

ectiv

e E

nerg

y

N=10

N=20

N=30

N=40

CAR improvements over MER (CAR/MER)

Efficient Data Communication Protocols for Wireless Networks DISSERTATION DEFENSE Engin Zeydan December 08, 2010 Advisor: Prof. Cristina Comaniciu (Stevens.

Documents

correlated data

data yi

data rate

data correlation

observed data

data accuracy

data redundancy

raw data