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
- 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