SIMPLY COOPERATIVE Anthony Ephremides Pompeu Fabra University April 29, 2010 Barcelona, Catalunia 1.

SIMPLY COOPERATIVE

Anthony Ephremides

Pompeu Fabra University

April 29, 2010

Barcelona, Catalunia1

THE “COAT OF ARMS”

S: source D: destination

2


R: relay


3


R: relay and source


4


R: relay and source


“ether” medium

5

THE “HISTORY”

6

THE “HISTORY”− “RELAY” CHANNEL (Van der Meulen ’60’s)

Key differencesNo “source” traffic from RNo “ether”Classical information-theoretic quest for capacity – backlogged S

reservoir

S D

R

7

THE “HISTORY”− “RELAY” CHANNEL (Van der Meulen ’60’s)

Key differencesNo “source” traffic from RNo “ether”Classical information-theoretic quest for capacity – backlogged S

− “REVISED” RELAY CHANNEL (wireless) − Laneman/Tse/Wornell

− Sendonaris /Erkip/Aazhang− Kramer/ Gastpar/Gupta− Kramer/Maric/Yates

Basic idea: Cooperative Diversity (variety of schemes) Objective: Again, Capacity (backlogged S)

(

)

reservoir

S D

R

8

……………………

A “WIRELESS” NETWORK PERSPECTIVE

9


• “PACKETS” THROUGHPUT

10



• “BURSTY TRAFFIC” DELAY

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− STABLE THROUGHPUT

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− STABLE THROUGHPUT− COGNITION (sensing)

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− STABLE THROUGHPUT− COGNITION (sensing)

Q: CAN’T WE STILL CO-OPERATE?

14

DIGRESSION: THE VIRTUE OF THE SINGLE QUEUE

(STATISTICAL MULTIPLEXING)or

1

2

M

D

1+2+…+M

DS

S1

S2

SM

15

“VIRTUAL” QUEUE

THE “PRIMITIVE” IDEA (Sadek, Liu, Ephremides 2007)

1

2

M

i

Relay

Source Terminals

Destination

S1

S2

Si

SM

R D

• NO CONTENTION (e.g. TDMA)

• PERFECT CHANNEL SENSING

• INSTANT ERROR-FREE “ACKs”

• SINR > • FADING CHANNELS (i.e. packet erasure

channels)

0

2||Pr

N

PhP ab

ab

16

hid

hir

hrd

17

COOPERATION METHOD 1• Each terminal transmits HOL packet in its assigned slot (if empty,

slot is free)

• If D receives successfully, it sends ACK (heard by both the relay and the user)

• If D does not succeed but R does: at first sensed empty slot R transmits to D the failed packet

• If neither D nor R succeed, packet gets retransmitted by the terminal in next frame

• Relay does not keep packets after the end of the frame

1. Relay has always a finite queue (M packets Max)

2. Terminal queues “interact”

Remarks:

Idle slots are utilized!

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COOPERATION METHOD 2• Each terminal transmits HOL packet in its assigned slot (if empty,

slot is free)

• If D receives successfully, it sends ACK (heard by both the relay and the user)

• If D does not succeed but R does: at first sensed empty slot R transmits to D the failed packet

• If neither D nor R succeed, packet gets retransmitted by the terminal at next opportunity

• Relay keeps all packets it receives correctly

1. Relay has a possibly growing queue

2. Terminal queues do not interact

Remarks:

Again: Idle slots are utilized!

THE CRITERION STABLE THROUGHPUT:

arrival rate service rate

Q(t): queue size at time t

0)(Prlim NtNtQ ~ “positive recurrence”

Loynes: If arrival process and service process are jointly stationary,

the queue is stable iff <

max stable throughput

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THE CRITERION (cont.)1

2

Q1(t)

Q2(t)

service

Problem: When Q1(t) and Q2(t) “interact”, stationary “service rate” cannot be identified.

Solution: STOCHASTIC DOMINANCE (Rao, Ephremides 1988)

Set of ’s such that Q1 and Q2 are stable

λ

1

2

Q1

Q2

1 1 1

1 1 1

1 1 1

2

2

2

2 2

2 2

2 2

1 1 1

1 1 1

2 2

2 2

1' 1' 1'2'

2'

2'

1 '≠ 1

2 '≠ 2

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BACK TO THE “PRIMITIVE” SYSTEM• COOP METHOD 1• COOP METHOD 2• RANDOM ACCESS• TDMA• SELECTIVE “DECODE-AND-FORWARD” ---NETWORK VIEW

EVERY PACKETUSES TWO SLOTS

OR

EVERY PACKETUSES TWO “HALF-SLOTS”AS TWICE THE RATE

i.e.

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nocooperation

BACK TO THE “PRIMITIVE” SYSTEM• COOP METHOD 1• COOP METHOD 2• RANDOM ACCESS• TDMA• SELECTIVE “DECODE-AND-FORWARD” ---NETWORK VIEW

EVERY PACKETUSES TWO SLOTS

OR

EVERY PACKETUSES TWO “HALF-SLOTS”AS TWICE THE RATE

i.e.

attention22

nocooperation

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RESULT FOR 2-USERS

Comparison

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

1

2TDMA

COOP2DF

ALOHA

COOP1

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DF: Relay transmits at the same rate and utilizes two time slots.

DF: Relay transmits at twice the rate and utilizes one time slots. (Rate and SNR-threshold are related through the Gaussian mutual information formula.

0 5 10 15 20 25 30 350

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

SNR Thresold () [dB]

Aggr

egat

e M

axim

um S

tabl

e Th

roug

hpt

TDMA=COOP1COOP2DFALOHA

1 2 3 4 5 6 7 8 9 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

R [b/s/Hz]

Aggr

egat

e M

ax S

tabl

e Th

roug

hput

TDMACOOP2DFALOHA

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DELAY• Notoriously difficult for interacting queues• Symmetric System: 2-users

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.410 0

10 1

10 2

10 3

10 4

10 5

1

Aver

age

Dela

y

TDMACOOP1COOP2DF

ALOHA

WHY?VIRTUE OF THE SINGLE QUEUE

1

2

M

D

S1

S2

SM

PARTIAL CONCENTRATION INTO SINGLE QUEUEIN METHOD 2

R

26

BUTS1

DS2

SM

R

27

BUTS1

DS2

SM

R DS2

SM

S1

28

BUTS1

DS2

SM

R DS2

SM

S1

1 N2 D =(N+1)

piNpND

ANY TERMINAL COULD PLAY THE ROLE OF THE RELAY

Pij: Packet success probability from i to j (increasing in i, decreasing in j, for i < j)

or, simply (PiD increasing in i)

TANDEM IS BORN piD

29

i

HENCE, BACK TO THE ‘COAT OF ARMS”

NEW ISSUE:

ACCESS POLICY:

PRIORITY ORDER IN SERVING QUEUES AT “2”− AFFECTS DELAY (NOT THROUGHPUT)

−“ANY” CONFLICT-FREE “WORK-CONSERVING”−TDMA (MAXIMUM STABLE THROUGHPUT REGION: SAME)−RANDOM OR SCHEDULED ACCESS WITH MULTIPACKET RECEPTION (B. Rong, A. Ephremides 2009)

1

2

1

2

3=D

p12

p13

p23

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STABLE THROUGHPUT REGION

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• Both policies yield same stable throughput regions under cooperation

• N users simultaneously increase stable throughput rates

• kmax1 ≤ k ≤ N-1

max

• p1,2 increases region increases

85.0,6.0,4.0,8.0,3.0 2,13,23,1 ppp

LESSON TAUGHT− GAIN BY ALL USERS BECOMES

MOTIVATION FOR COOPERATION

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MOTIVATION FOR COOPERATION or

− IT IS IN THE INTEREST OF THE RICH TO HELP THE POOR

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MOTIVATION FOR COOPERATION or

− IT IS IN THE INTEREST OF THE RICH TO HELP THE POOR

Deeper and Far-reaching Interpretation:FOR BURSTY TRAFFIC IN SHARED CHANNELS, REDUCTION OF THE PRESENCE OF COMPETITION IS BENEFICIAL

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SEQUEL• STABLE THROUGHPUT REGION

“BACKLOGGED” THROUGHPUT REGION

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(FOR SCHEDULED ACCESS AND PRIORITY TO “NOT-TO-RELAY”)

− COMMON PHENOMENON

• FOR RANDOM ACCESS (q1,q2) ON COLLISION CHANNEL, COOPERATION MAY HELP

IF

vs

2231312

1313122313

1

)1(

ppp

ppppp

TS

NCS

COOPS

(B. Rong, A. Ephremides ISIT 2009)

S

T

MULTI-PACKET RECEPTION CAPABILITY

• CRITERION: SINR > (simplest)• NEW SET OF SUCCESS PROBABILITIES• NO SIMULTANEOUS “TRANSMIT” AND “RECEIVE” BY R (initially)• PSR AS BEFORE• PRD > PRD/S new

PSD > PSD/R new

and of course PRD > PSD (Denote these probabilities by )

• R KNOWS WHETHER QS=0

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(B. Rong, A. Ephremides 2009)

COOPERATION POLICY: I. R MIXES OWN AND S’s PACKETSII. IF QS=0, R TRANSMITS w.p. 1 (IF QR>0)III.IF QS>0, S TRANSMITS w.p. 1 AND R w.p. q (IF QR>0)

p

“Standard” channel(J. Luo & A. Ephremides 2006)

R

S D

RESULT (MPR)

A REGION OF VALUES OF THE PACKET

SUCCESS PROBABILITIES, ,SUCH THAT

① IF

② IF for q=0

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Λ

Λp NCS

COOPS

Λp NCS

COOPS

for suitable values of q

(i.e., scheduled transmission or “conventional” cooperation )

RESULT (cont.)

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0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.450

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

1 [packets/slot]

2 [pac

kets

/slo

t]

NC

CC, C-OPP

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.450

0.1

0.2

0.3

0.4

0.5

0.6

0.7

1 [packets/slot]

2 [pac

kets

/slo

t]

NC

CC

C-OPP

If , opportunistic scheme results in improved stability region

If , the optimal strategy is the conventional cognitive cooperation

Resulting stability regions

Λp Λp

--- AND MORE• SIMILAR RESULTS FOR FULL TANDEM (MORE

THAN TWO SOURCE TERMINALS)

• ENHANCEMENT WITH PHYSICAL-LAYER IMPROVEMENTS– COMBINE WITH DYNAMIC DECODE-AND-FORWARD

(K. Azarian, H. El Gamal, P. Schniter 2005)

– COMBINE WITH ADAPTIVE SUPERPOSITION CODING

(T. Cover 1972)

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(B.Rong, I. Krikidis, A. Ephremides 2009)

RESULT

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NC: no cooperation CC: conventional cooperationS-CC: conventional cooperation with superposition codingNC-DDF: non-cognitive DDF C-DDF: cognitive DDFSC-DDF: cognitive DDF with superposition coding

WHAT ABOUT NETWORK CODING?

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S

R

1

2

D

QR1

QR2

transmits random linear combinations of contents of QR1 , QR2 (packet-by-packet)

−NO IMPROVEMENT

--BUT: (i) IF THERE ARE MULTIPLE DESTINATIONS AND / OR (ii) CONTENTS OF BUFFERS ARE COMBINED IN THEIR ENTIRETY

− POSSIBLE IMPROVEMENT (under investigation)

R:

CONCLUSION− RELAY-BASED COOPERATION AT THE

PACKET LEVEL CAN BE BENEFICIAL FOR DIFFERENT REASONS (NOT DIVERSITY-RELATED)

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CONCLUSION− RELAY-BASED COOPERATION AT THE

PACKET LEVEL CAN BE BENEFICIAL FOR DIFFERENT REASONS (NOT DIVERSITY-RELATED)

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SIMPLY COOPERATIVE

−TERMINALS CAN BE

SIMPLY COOPERATIVE Anthony Ephremides Pompeu Fabra University April 29, 2010 Barcelona, Catalunia 1.

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