september 19-20, 2005© seil 20051 progress summary “dawn” muri review anthony ephremides...

September 19-20, 2005 © SEIL 2005 1

Progress Summary

“Dawn” MURI Review

Anthony EphremidesUniversity of Maryland

Santa Cruz, CASeptember 12, 2006

© HyNet 2006 2

OUTLINE

• Over-Riding Theme: Layer Integration & Theoretical Foundations

– Physical layer incorporation into MAC and beyond

1) Capture

2) Alternative Access/Receiver Comparison

3) Multicast Stability/Capacity

4) Tandem Network Stability/CapacityNetworkCoding

© HyNet 2006 3

(1) On Capture (with J. Wieselthier & G. Nguyen)

• Essence: – Bridging The Gap Of Networking And

Communication-Information-Theoretic Approach To Multiple Access via the SINR Tool

– Correcting Previous Analyses For Capture Probability Derivation

© HyNet 2006 4

Random-Access System

• Collision channel – no capture

• General Multiple-Access channel – all users “succeed”

• In-between: Reception in the presence of interference– SINR-based model

• One or more users can be successful

Receiver

© HyNet 2006 5

Capture Probability

• Capture probability:

– Cn = Pr{at least one transmission is successful

| n simultaneous transmissions}

• Expected number of successful packets in a slot:– Sn = E{number of successful packets | n simultaneous transmissions}

• Multi-Packet reception capability– Depends on detector

Receiver

© HyNet 2006 6

SINR-based Capture Model

• A packet from user j is successful if and only if

b = 0: Perfect capturesingle detector: largest always successfulmultiple detectors: all are successful

b = ∞: No capture (collision channel)when 2 or more transmit, none are successful

SINR( j)P( j)

N P(i)i1,ij

n

b

P(j) = Power at receiving node from user j

b = Threshold that depends on many system parameters (increasing function of rate)

Receiver

j

© HyNet 2006 7

Earlier Work (Zorzi & Rao, JSAC 1994)

• t = test user

• Pn(r0) = Pr{SINR(t) > b | rt = r0}

• h(r0) = pdf of r0 (distance of user to base station)

(*) is not valid for b < 1

Implicitly assumes only one signal can satisfy SINR

Example:

• Propagation loss factor = 4

• Fading and shadowing are present

*which exceeds 1 when

Cn nPr{SINR(t) b} nPn(r0 )h(r0 )dr0

0

1

C

2

b

b

4

2

(*)

00.5

11.5

22.5

33.5

44.5

5

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1b

C

© HyNet 2006 8

Extend Model toAccommodate All Values of b

Observations• More than one user can satisfy SINR > b when b < 1 Interesting case

• Cn = Pr{one or more users satisfy SINR condition}

= Pr{largest signal satisfies SINR condition}

• Let user M be the one with the largest signal

*Thus, Cn = Pr{SINR(M) > b}

• Since all users are equally likely to be the largest

*Cn = n Pr{SINR(1) > b, M = 1}

© HyNet 2006 9

Analytical Evaluation of Capture Probability

• Cn = n Pr{SINR(1) > b, M = 1} = Pr{SINR(M) > b}

*where M is the user with largest received power

• Example:

*For

• In general,

Cn n 1 ...0

FP max (b x j ),x2 ,x3,..,j2

n

xn

0

0

dFP (x2 )dFP (x3)...dFP (xn )

where

FP is the common cdf of the received power levels (which are i.i.d.)

P( j)PT r , C2

1 if b1

b 2/ if b 1

© HyNet 2006 10

Simulation is Neededto Evaluate Cn

• Users uniformly distributed in disk of radius = 1– No fading or shadowing:

• any propagation model can be accommodated

• Results for b > 1 are same as those obtained by others

0

0.2

0.4

0.6

0.8

1

1 10 100 1000number of transmitted packets (n)

b = 0

b = 0.1

b = 0.2

b = 0.5

b = 1

b = 2

b = 10

0

0.2

0.4

0.6

0.8

1


b = 0.2

b = 0.5

b = 1

b = 2

b = 10

PR PT r

PR

PT

r2

PR

PT

r4

The model is not realistic!Valid only in far-field regionReceived power approaches ∞ as r approaches 0

PR PT r

© HyNet 2006 11

More-RealisticPhysical Model

• Assume users are uniformly distributed in a circular region of radius = 10. No fading.

0

0.2

0.4

0.6

0.8

1


b = 0

b = 0.1

b = 0.2

b = 0.5

b = 1

b = 2

b = 10

0

0.2

0.4

0.6

0.8

1


b = 0b = 0.1

b = 0.2b = 0.5

b = 1

b = 2

b = 10

PR PT (1 r)

• Curves for Cn are drastically different from those for Previously described performance is not correct Overestimates received power when transmitter is close to receiver

PR PT r

= 2 = 4

0

1

2

3

4

0 1 2 3 4 5r

= 2instead of PR PT r

© HyNet 2006 12

Multi-Packet Reception

• All packets for which SINR > b are successful– Not only the largest

• Sn = n Pr{SINR(1) > b}

0

1

2

3

4

5


b = 0

b = 0.1

b = 0.2

b = 0.5

b = 1b = 2b = 10

0

1

2

3


b = 0

b = 0.1

b = 0.2

b = 0.5

b = 1

b = 2b = 10

PR 1

1 r 2

PR 1

1 r 4

= 10

© HyNet 2006 13

A Network with Two Destinations

• Users uniformly distributed throughout union of 2 circles of radius • One destination receiver in each circle

– Separated by distance d

• Traffic distribution

– Each packet has a specific destination (receiver)

• Does not add to throughput when decoded at “wrong” receiver

• Adds to interference at both receivers

– In intersection of 2 circles

• Packet is equally likely to be intended for D1 or D2

– In rest of region

• Packet is intended for closer destination

.D1. D2

d

© HyNet 2006 14

Cn for Two-Destination Network

.D1. D2

d

0

0.2

0.4

0.6

0.8

1


b = 10

b = 2

b = 1

b = 0.5

b = 0.2

b = 0.1

b = 0

0

0.2

0.4

0.6

0.8

1


b = 10

b = 2

b = 1

b = 0.5

b = 0.2

b = 0.1

b = 0

d = 20 (circles just touching) d = 15 (circles overlap)

• = 10

• n1 = n2 = n (i.e., same number of packets for each destination)

•

PR 1

1 r 2

Results demonstrate impact of “broader interference” effect resulting from overlapping user populations

© HyNet 2006 15

(2) Alternative Access-Receiver Comparison

(joint work with Jie (Rockey Luo)

• Essence: – Comparison of Scheduled and Simultaneous

(Parallel) Multiple Access Strategies

– Two Low-Complexity Schedules: TDMA PMAS

– Spectral Efficiency vs. Energy Cost comparison

– PMAS Dominates if Multiple Antennas are Available at the Receiver

© HyNet 2006 16

Three Channel Sharing Schemes

Optimal(complex)

Parallel transmission, Multiuser decoding.

TDMA (simple)

Sequential transmission

PMAS (simple)

Parallel transmission, Single user decoding.

Joint Decoding

Rsum=log[1+iPi /N0]

SNRi=Pi /(N0+jiPj)

Single user Decoding

Gaussian noise of power N0

Pi is the transmit power of user i. All channels have unit gain.

© HyNet 2006 17

Spectral Efficiency Comparison

1 1.2 1.4 1.6 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Energy Cost: E (Joule/nat)

Spe

ctra

l Eff

icie

ncy:

R (

nat/s

ec/B

Hz)

PMAS

OPT & TDMA

approximately half spectral efficiency

10 transmitters, time-invariant channel, channel gains randomly generated, transmitters know channel states

1 1.2 1.4 1.6 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Energy Cost: E (Joule/nat)

Spe

ctra

l Eff

icie

ncy:

R (

nat/s

ec/B

Hz)

PMAS & TDMA

OPT

10 transmitters, time-variant channel, independent Rayleigh fading, transmitters do not know channel states

approximately half spectral efficiency

Comparing the three schemes: Optimal, TDMA and PMAS

© HyNet 2006 18

Comparison on System Slopes

1 2 3 4 5 6 7 8 9 10 0

1

2

3

4

5

6

7

8

9

10

Number of Receive Antennas

Sys

tem

Slo

pe

PMAS

OPT

TDMA

MK

MK

EE

S

F

ii

Hiii

OPT

222

2

0

h

hhθ

12

22

22

242

2

0

MK

MK

E

E

EE

S

i

i

ii

F

ii

Hiii

PMAS

h

h

h

hh

1

222

2

40

M

M

E

E

S

ii

ii

TDMA

h

h

10 transmitters, time-variant channel, Rayleigh fading, CDI at the transmitterK: number of transmittersM: number of receive antennas

We can exploit space resource at the receiver!

© HyNet 2006 19

Superiority of PMAS over TDMA

General Results : PMAS is better than TDMA !

In low power regime, let # of terminals ∞ RPMAS ROPT / 2 ROPT, RPMAS # receive antennas RTDMA constant

• Multiantenna sampling creates a multi dimensional image.

• Nature helps separating signals (multiuser multiplex gain)

• Orthogonal channel sharing is inefficient in exploiting multiuser multiplex gain.

© HyNet 2006 20

Summary

The dominance of TDMA is due to its simplicity.

1.1.

Orthogonal channel sharing is inefficient in exploiting multiuser multiplex gain. Such inefficiency can be significant in the low power regime.

2.2.

Overcoming this inefficiency with simple alternative is the key challenge. We showed that such alternative exists in low power regime multiple access systems.

3.3.

© HyNet 2006 21

(3) Multicast Stability/Capacity(joint work with B. Shrader and Y. Sagduyu)

• Essence: – Extension of Collision Channel Results

– Stability Region Capacity Region

– Simple Network coding Scheme Extends Stability Region to the Capacity Region

© HyNet 2006 28

(4) Tandem Network Stability/Capacity (via Network coding)

(joint work with Y. Sagduyu)

• Essence: – Joint Access/Network coding Broadcasting

over Wireless Tandem Networks

– Focus on Stable Throughput

– Extensions (Cooperative/Competitive Strategies, Energy Optimization)

© HyNet 2006 29

• Tandem network:

• Multiple sources.

• Error-free transmissions & Mostly broadcasting.

• Case 1: Assume continuously generated packet traffic, i.e. saturated packet queues.

– With or without Network Coding, Find Maximum Throughput Region.

• Case 2: Allow packet queues to empty.

– With or without Network Coding, Find Maximum Stable Throughput Region.

Model and Objectives

i,j : average rate (packets/s)

i j

© HyNet 2006 30

• Three separate

queues at node i:

• Plain Routing: Network Coding:

Tandem Wireless Network Model (Saturated Queues)

• Scheduled Access: Group 1: 1, 4, 7, …, Group 2: 2, 5, 8, …, Group 3: 3, 6, 9, …

Activate node group m over disjoint fractions of time tm , m {1,2,3}.

• Random Access: Node i transmits (new or collided) packets with fixed probability pi .

(Crucial Point)

1 2 3 n -1 n4 5 6

Qi1 stores source packets node i generates.

Qi2 stores relay packets from right neighbor of node i

Qi3 stores relay packets from left neighbor of node i

+

orQi1

Qi2

Qi3

or

or

Qi1

Qi2

Qi3

Qi3

Qi1

Qi2

(Linear combination)

© HyNet 2006 31

Achievable Throughput Region under Scheduled Access

routingplain for ,,

codingnetwork for ,, ,

)(

)()(

Nit

Nitt

iml

ir

ii

iml

iiimr

ii

ir and i

l : total rates of packets arriving at node i from right and left neighbors.

i : throughput rate from node i to destinations Mi.

• Throughput rates satisfy:

• Achievable throughput

region A includes s.t.:

For n = 3, achievable

throughput region A is:

3

1 )(:

3

1 )(:

routingplain for 1}{max

codingnetwork for 1}),max({max

m

li

rii

mimi

m

li

rii

mimi

© HyNet 2006 32

• Allow packet queues to empty.

– Packet underflow possible: node can wait to perform Network Coding or proceed with Plain Routing.

– Consider two dynamic strategies based on instantaneous queue contents:

• Strategy 1: Every node attempts first to transmit relay packets and

transmits a source packet only if both relay queues are empty.

• Strategy 2: Every node attempts first to transmit a source packet and

transmits relay packets only if the source queue is empty.

– Strategy 2 expands the stability region STR(S) to the boundary of TR(A).

Stable Throughput Region under Scheduled Access

routingplain forcoding,network for11 )()()(

)( iml

ir

iiim

li

im

ri

imi ttt

t

routingplain forcoding,network for),max( )()( iml

ir

iiiml

ir

ii tt

© HyNet 2006 33

• Deriving the achievable and stable throughput regions A and S is difficult.

– Throughput regions depend on the transmission schedules t.

• Consider alternative measures:

• Assume saturated queues (or non-saturated queues together with strategy 2.).

•

Alternative Optimization Measures

i iiii M ||}{minmin

Minimum transmitted throughput “Sum”-delivered throughput

tt ,

min,

maxargmaxarg

• Find best schedule t to maximize min or over A or S.

© HyNet 2006 34

Throughput Optimization Results

• For broadcasting

2 4 6 8 10 12 14 16 18 200

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

number of nodes n

thro

ughput per

sourc

e-d

est

inatio

n p

air

Network coding for optimal min

Plain routing for optimal min

Network coding for optimal

Plain routing for optimal

with Mi = N – {i}, i N :

min = 0 for optimal values of .

Network coding doubles .

No improvement in min,

as n increases.

Objectives of maximizing min and under broadcast communication cannot be achieved simultaneously.

© HyNet 2006 35

Extension to Random Access

• Assume saturated queues (otherwise, the problem involves interacting queues).

– Nodes randomize between waiting or transmitting source packets or relay packets.

– Source packet transmissions:

A: Transmit new source packets at any time slot (no feedback - possible loss)

B: Transmit source packets until they are received by both neighbors (feedback + repetition)

C: Transmit linear combinations of source packets (feedback + coding) :

4 6 8 10 12 14 16 18 200

0.02

0.04

0.06

0.08

0.1

0.12

0.14

number of nodes n

thro

ughp

ut p

er s

ourc

e-de

stin

atio

n pa

ir

Network coding with method A

Network coding with method B

Network coding with method C

Plain routing with method A

Plain routing with method B

Plain routing with method C

Packet remains in queue Qi1.

Packet enters queue Qi2.

Packet enters queue Qi3.

© HyNet 2006 36

Wrap-Up

• Four Inter-Related Sets of Contributions

• Physical Layer Role in MA

• Network coding in Wireless Multicast Environments

• Stable Throughput Region Focus

© HyNet 2006 37

Plans

• Convert Throughput Results (packets/s) to Spectral Efficiencies (bits/s)

• Scheduling versus Parallel Transmission (with or without Network Coding)

• Packet Erasure Channel Models to be Broadened

• Connect Delay Analysis to Back-Pressure Algorithm

september 19-20, 2005© seil 20051 progress summary “dawn” muri review anthony ephremides...

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