Selection Metrics for Multi-hop Cooperative Relaying

Jonghyun Kim

and

Stephan Bohacek

Electrical and Computer Engineering

University of Delaware

Contents

• Introduction• Diversity• Goal of Cooperative Relaying• Brief look at how to overcome challenge• Dynamic programming• Simulation environment• Selection Metrics• Differences between Selection Metrics• Conclusion and Future/current Work

Introduction

source destination

One possible path

Introduction

source destination

Another possible path

Introduction

source destination

- Not all paths are the same- The “best” path will vary over time

Many possible path

Diversity

• Link quality and hence path quality can be modeled as a stochastic process1. If there are many alternative paths, there will be some

very good path2. The best path changes over time

Goal of cooperative relaying

• Take advantage of diversity (Don’t get stuck with a bad path Switch to a good (best) path)

Challenge

• How to find and use the best path with minimal overhead

Potential benefits

• The focus of this talk

Brief look at how to overcome the challenge

(2,1)

(2,2)

(1,1)

(1,2)

source destination

relay-set (1)relay-set (2)

Nodes within relay-set (2) have decoded data from source

Brief look at how to overcome the challenge

(2,1)

(2,2)

(1,1)

(1,2)

source destination

relay-set (1)relay-set (2)

- Nodes within relay-set (2) simultaneously broadcast RTS with a different CDMA code

RTS

Brief look at how to overcome the challenge

(2,1)

(2,2)

(1,1)

(1,2)

source destination

relay-set (1)relay-set (2)

- Nodes within relay-set (1) receive RTSs and make channel gain measurements- R(n,i),(n-1,j) : channel gain from node (n,i) to (n-1,j)

R(2,1),(1,1)

R(2,2),(1,2)

RTS

R(2,2),(1,1)

R(2,1),(1,2)

Brief look at how to overcome the challenge

(2,1)

(2,2)

(1,1)

(1,2)

source destination

relay-set (1)relay-set (2)

R(2,1),(1,1) R(2,2),(1,1) J(1,1)

R(2,1),(1,2) R(2,2),(1,2) J(1,2)

CTS

- Nodes within relay-set (1) broadcast CTS- CTS contains channel gain measurements and J- J encapsulates downstream channel information (to be discussed later)

Brief look at how to overcome the challenge

(2,1)

(2,2)

(1,1)

(1,2)

source destination

relay-set (1)relay-set (2)CTS

- All nodes within relay-set (2) have the same information

R(2,1),(1,1) R(2,1),(1,2)

R(2,2),(1,1) R(2,2),(1,2)

J(1,1) J(1,2)

R(2,1),(1,1) R(2,1),(1,2)

R(2,2),(1,1) R(2,2),(1,2)

J(1,1) J(1,2)Channel matrix

Brief look at how to overcome the challenge

(2,1)

(2,2)

(1,1)

(1,2)

source destination

relay-set (1)relay-set (2)DATA

- Based on this information, the nodes within relay-set (2) all select the same node to transmit the data

- If node (2,1) is selected, it broadcasts the data

Brief look at how to overcome the challenge

(2,1)

(2,2)

(1,1)

(1,2)

source destination

relay-set (1)relay-set (2)

- The process repeats- Best-select protocol (BSP)

DATA

Dynamic programming

- Various meanings of J• Probability of packet delivery• Minimum channel gain through the path• Minimum bit-rate through the path• End-to-end delay• End-to-end power• End-to-end energy

J(n,i) is the “cost” from the ith node in the nth relay-set to destination

J(n,i) = f (R(n,1),(n-1,1) , R(n,1),(n-1,2) , …. , R(n,i),(n-1,j) , J(n-1,1) , J(n-1,2) , … , J(n-1,j))

Js from the downstream relay-set

Channel gains

Costs to goStage costs

Simulation environment

- Idealized urban BSP # of nodes Mobility Channel gains Area Tool used

: 64, 128: UDel mobility simulator (realistic tool): UDel channel simulator (realistic tool): Paddington area of London: Matlab

- Implemented urban BSP # of nodes Mobility Channel gains Area Tool used

: 64, 128: UDel mobility simulator: UDel channel simulator: Paddington area of London: QualNet

UDel mobility simulation

• Current Simulator– US Dept. of Labor Statistics time-

use study• When people arrive at work• When they go home• What other activities are

performed during breaks

– Business research studies• How long nodes spend in

offices• How long nodes spend in

meetings

– Agent model• How nodes get from one

location to another• Platooning and passing

• Signal strength is found with beam-tracing (like ray tracing)

• Reflection (20 cm concrete walls)

• Transmission through walls• Uniform theory of diffraction• Indoors uses the Attenuation

Factor model • No fast-fading• No delay spread• No antenna considerations

Propagation during a two minute walk

UDel channel simulation

Selection Metrics

Maximizing Delivery Prob. ( J = Delivery Prob.)

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

nn InIninin JXRfJ

))2(,1())2(,1(),,())1(,1(),,( )1(11

)())(1(nnn InIninInin JXRfXRf

The best J in relay-set (n) :

Data sending node

)( ),(),( max ini

kn JJ

: node (n,k)

- X - f(V)-

1nI

: transmission power which is fixed in this metric: prob. of successful transmission: an order of the nodes in the (n-1)-th relay-set such that

))2(,1())1(,1( )1()1( nn InIn JJ

Selection Metrics

Maximizing Delivery Prob. ( J = Delivery Prob.)

min relay-set size

impr

ovem

ent i

n er

ror

prob

. (ra

tio)

2 4 6 8 100

0.2

0.4

0.6

0.8

1

SparseDense

idealized urban

- This plot show the error prob. (i.e., 1- J(n,i) )- X-axis : minimum relay-set size along the path from source to destination- Y-axis : Avg( (1-J(n,1) )BSP/(1-J(n,1) )Least-hop ) J(n,1) is source’s J- Comparison stops once the least-hop path fails

Selection Metrics

Maximizing Minimum Channel Gain ( J = Channel Gain )

)),(( ),1(),1(),,(),( minmax jnjninjj

in JRJ

The best J in relay-set (n) :

Data sending node

)( ),(),( max ini

kn JJ

: node (n,k)

- The link with the smallest channel gain can be thought of as the bottleneck of the path.- The objective is to select the path with the best bottleneck

Selection Metrics

Maximizing Minimum Channel Gain ( J = Channel Gain )im

prov

emen

t in

chan

nel g

ain

(dB

)

min relay-set size

2 4 6 8 100

5

10

15

20

25

30 SparseDense

idealized urban implemented urban

2 4 6 8 100

5

10

15

20

25

30

- Y-axis : Avg( (min channel gain)BSP - (min channel gain )Least-hop )

Selection Metrics

Maximizing Throughput ( J = Bit-rate )

)),(( ),1(),( minmax jnjj

in JBJ

)_1),(:( ),1(),,(max PERTARGETrateBitXRfrateBitB jninrateBit

- Bit-rate : 1Mbps, 2Mbps, 4Mbps, 6Mbps, 8Mbps, 10Mbps,12Mbps- The objective is to select the path with the best bottleneck in terms of bit-rate

The best J in relay-set (n) :

Data sending node

)( ),(),( max ini

kn JJ

: node (n,k)

Selection Metrics

Maximizing Throughput ( J = Bit-rate )

min relay-set size

impr

ovem

ent i

n th

roug

hput

(ra

tio)

2 4 6 8 100

5

10

15SparseDense

2 4 6 8 100

5

10

15

idealized urban implemented urban

- Y-axis : Avg( (min bit-rate)BSP / (min bit-rate )Least-hop )- Least-hop approach uses the fixed bit-rate

Selection Metrics

Minimizing End-to-End Delay ( J = Delay )

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

)( ))2(,1(),,())1(,1(),,())1(,1(),,(),( 111

BXRfBXRfBXRfB

sizepacketBJ

nnn IninIninIninin

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

nn InInin JBXRf

)),()),(1( ))2(,1())2(,1(),,())1(,1(),,( )1(11

nnn InIninInin JBXRfBXRf

))),(1))(,(1(( ))2(,1(),,())1(,1(),,( 11

BXRfBXRfTnn IninInin

The best J in relay-set (n) : )( ),(),( min ini

kn JJ

: node (n,k)

)(),(),( min BJJ inB

in

Data sending node

- Delay to next relay-set (if the transmission is successful) - Delay from next relay-set to destination (depends on which node was able to decode)- If no node in the next relay-set succeeds in decoding, then a large delay T is incurred due to transport layer retransmission

Selection Metrics

Minimizing End-to-End Delay ( J = Delay )

min relay-set size

impr

ovem

ent i

n de

lay

(rat

io)

2 4 6 8 100

5

10

15 SparseDense

2 4 6 8 100

5

10

15

idealized urban implemented urban

- Y-axis : Avg( (end-to-end delay)Least-hop / (end-to-end delay )BSP )

Selection Metrics

Minimizing Total Power ( J = Power )

)*( ),1(),1(),,(),( min jnjninj

in JRCHJ

The best J in relay-set (n) :

Data sending node

)( ),(),( min ini

kn JJ

: node (n,k)

- CH* : per link channel gain constraint- If a node transmits a data with power X (dBm)= CH* - R(n,I),(n-1,j) , then channel gain constraint will be met E.g.) CH* = -86 dBm, R (n,I),(n-1,j) = -60dBm X(dBm) = -86 – (-60) = -26

Selection Metrics

Minimizing Total Power ( J = Power )

min relay-set size

impr

ovem

ent i

n po

wer

(ra

tio)

2 4 6 8 10100

101

102

103

104

2 4 6 8 10100

101

102

103

104

idealized urban implemented urban

SparseDense

- Y-axis : Avg( (end-to-end power)Least-hop / (end-to-end power )BSP )- Least-hop approach uses the fixed transmission power

Selection Metrics

Minimizing Total Energy ( J = Energy )

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

),( ))2(,1(),,())1(,1(),,())1(,1(),,(),( 111

BXRfBXRfBXRfB

sizepacketXXBJ

nnn IninIninIninin

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

nn InInin JBXRf

)),()),(1( ))2(,1())2(,1(),,())1(,1(),,( )1(11

nnn InIninInin JBXRfBXRf

))),(1))(,(1(( ))2(,1(),,())1(,1(),,( 11

BXRfBXRfMnn IninInin

The best J in relay-set (n) : )( ),(),( min ini

kn JJ

: node (n,k)

),(),(,

),( min XBJJ inXB

in

Data sending node

- Energy to next relay-set- Energy from next relay-set to destination- M represents the energy required to retransmit the packet due to transport layer retransmission- Best node will transmit a data with power X and bit-rate B

Selection Metrics

Minimizing Total Energy ( J = Energy )

min relay-set size2 4 6 8 1010

0

101

102

103

impr

ovem

ent i

n en

ergy

(ra

tio)

SparseDense

2 4 6 8 10100

101

102

103

idealized urban implemented urban

- Y-axis : Avg( (end-to-end energy)Least-hop / (end-to-end energy )BSP )- Least-hop approach uses the fixed transmission power and bit-rate

Differences between Selection Metrics

2 4 6 8 100

0.2

0.4

0.6

0.8

1

frac

tion

of r

elay

s sh

ared

mean size of relay-set

Max Delivery Prob. vs. Max-Min Channel GainMin Delay vs. Max ThroughputMin Total Power vs. Min Energy

- On average about 40% of the paths are shared when mean size of relay-set is 2- The bigger mean size of relay-set, the more the paths are disjoint- While metrics all use the channel gain, different meanings of metrics lead to difference in the paths selected

Conclusion and Future Work

• Reduce overhead of RTS/CTS control packets• Investigate optimum size of relay-set• Better method of joining, leaving relay-set and detecting route failures

• Diversity allows BSP to achieve significant improvement in various metrics • Recall that in physical layers such as 802.11 received power varies

over a range of 5-6 orders of magnitude (-36 dBm to -96 dBm). That is, a good link may be 100,000 ~ 1,000,000 times better than a bad link.

• In communication theory, the link is given, regardless of whether the link is bad or good.

• In networking, we do not have to use the bad links; we can pick links that are perhaps 100,000 ~1,000,000 times better

Future/current Work

Conclusion

Webpage of our group : http://www.eecis.udel.edu/~bohacek/UDelModels/index.html