Download - Link Layer: Wireless Mesh Networks Capacity
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Link Layer:Wireless Mesh Networks
Capacity
Y. Richard Yang
11/13/2012
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Outline
Admin. and recap Wireless mesh network capacity Maximize mesh capacity
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Admin.
Exam Average (mean): 68.6; max = 74
Project check point 1 Sending email to [email protected] Includes contents on
• references• setting
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Recap: Wireless Link Access Control Problem: single shared medium,
hence if two transmissions overlap on all dimensions [time, space, frequency, and code], then it is a collisionSlotted ALOHA Ethernet
Hidden-terminalCollision detection/prevention
Zigzag decoding
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Recap: 802.11 CSMA/CA
data
waitB1 = 5
B2 = 15
B1 = 25
B2 = 20
data
wait
B1 and B2 are backoff intervalsat nodes 1 and 2cw = 31
B2 = 10busy
busy
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Recap: ZigZag Decoding
Exploits 802.11’s behavior Retransmissions
Same packets collide again Senders use random jitters
Collisions start with interference-free bits
∆1 ∆2Pa
Pb
Pa
Pb
Interference-free Bits
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ZigZag Algorithm
∆1 ∆2
while (exists a chunk that is interference-free in one collision and has interference in the other) {
decode and subtract from the other collision
}
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∆1 ≠∆2
11
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∆2
11
22
11
∆1
How Does ZigZag Work?
∆1 ≠∆2 while (exists a chunk that is interference-free in one
collision and has interference in the other) {
decode and subtract from the other collision
}
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∆211
2222∆1
How Does ZigZag Work?
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∆1 ≠∆2 while (exists a chunk that is interference-free in one
collision and has interference in the other) {
decode and subtract from the other collision
}
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∆211
22 44∆1
How Does ZigZag Work?
33 33
∆1 ≠∆2 while (exists a chunk that is interference-free in one
collision and has interference in the other) {
decode and subtract from the other collision
}
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∆211
22 4444∆1
How Does ZigZag Work?
33 55
∆1 ≠∆2 while (exists a chunk that is interference-free in one
collision and has interference in the other) {
decode and subtract from the other collision
}
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∆211
66∆1
How Does ZigZag Work?
33 55 55
22 44
∆1 ≠∆2 while (exists a chunk that is interference-free in one
collision and has interference in the other) {
decode and subtract from the other collision
}
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∆211
6666∆1
How Does ZigZag Work?
22 44
33 55 77
∆1 ≠∆2 while (exists a chunk that is interference-free in one
collision and has interference in the other) {
decode and subtract from the other collision
}
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∆2
11
66 88∆1
How Does ZigZag Work?
22 44
33 55 7777
∆1 ≠∆2
Delivered 2 packets in 2 timeslotsAs efficient as if the packets did not collide
while (exists a chunk that is interference-free in one collision and has interference in the other) {
decode and subtract from the other collision
}
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Implementation
• USRP Hardware• GNURadio software• Carrier Freq: 2.4-2.48GHz• BPSK modulation
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USRPsTestbed
• 10% HT,
• 10% partial HT,
• 80% perfectly sense each other
802.11a
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Throughput Comparison
802.11
Throughput
CD
F o
f co
ncur
rent
flo
w p
airs
Hidden Terminals
Partial Hidden Terminals
Perfectly Sense
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Throughput Comparison
ZigZag
Throughput
CD
F o
f co
ncur
rent
flo
w p
airs
802.11
Hidden Terminals get high throughput
ZigZag Exploits Capture Effect
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Capture EffectSubtract Alice and combine Bob’s packet
across collisions to correct errors
∆1 ∆2Pa1
Pb
Pa2
Pb
3 packets in 2 time slots better than no collisions
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Summary
Basic lesson: Traditional thinking was on avoiding
collisions Zigzag changed the way of thinking:
decoding collisions
Many extensions of the Zigzag idea: decoding collisions, instead of avoiding collisions See Remap in Backup Slides
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Infrastructure Mode Wireless
APAP
AP wired networkAP: Access Point
Problems of infrastructure mode wireless networks?
802.11 by default operates in infrastructure mode.
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Mesh Networks
ad-hoc (mesh) mode
APAP
AP wired networkAP: Access Point
fast and low-cost deployment no central point of failure no APs overhead for users
who can reach each other
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Outline
Admin. and recap Wireless mesh network capacity
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Capacity of Mesh Networks
The question we study: how much traffic can a mesh wireless
network carry, assuming an oracle to avoid the potential overhead of distributed synchronization (MAC)?
Why study capacity? learn the fundamental limits of mesh
wireless networks separate the spatial reuse perspective and
system design perspective gain insight for designing effective wireless
protocols
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Mesh Transmission Constraints
transmission successful if there are no other transmitters within a distance (1+)r of the receiver
receiver
sender
r(1+)r
Interference constraint a single half-duplex
transceiver at each node: either transmits or
receives transmits to only one
receiver receives from only
one sender
Radio interface constraint
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Model
Domain is a disk of unit areaThere are n nodes in the domainThe transmission rate is W bits/sec
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Capacity of Mesh Wireless Network
Consider two types of networks
arbitrary networks: place nodes optimally to derive overall upper bound
random network: nodes are placed randomly
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Outline
Admin Wireless mesh network capacity
setting arbitrary networks: place nodes optimally to
derive overall upper bound
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Transmission Model: Bit-time Perspective Chop time into a total of WT bit-times in T
seconds The transmission decision is made for each
bit
bit time 2 bit time t bit time WTbit time 1
1
2
3
5
4
1
2
3
5
4
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Transmission Model: End-to-end Perspective Assume the network sends a total of T end-to-
end bits in T seconds Assume the b-th bit makes a total of h(b) hops from the
sender to the receiver Let rb
h denote the hop-length of the h-th hop of the b-th bit
2
1
2
T
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Hop-Count Constraint
Since there are a total of WT bit-times, and during each bit-time there are at most n/2 simultaneous transmissions, we have
T
b
WTnbh
1 2)(
2
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m
k
(1+)r’
r’
Area Constraint Consider two simultaneous
transmissions at a bit-time
i
j
(1+)r
r
Djm + r >= Dim >= (1+)r’
Djm >= (r+r’) /2
Djm + r’ >= Djk >= (1+)r
½ r
½ r’
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Area Constraint
For each transmissionwith distance r from sender to receiver, we draw a circle with radius ½ r
These circlesdo not overlap
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Area Constraint: Global Picture
2
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Area Constraint: Global Picture
sum over all circles, since each circle has at least ¼ of its area in the unit disk,
2
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Summary: Two Constraints
transmission successful if there
are no other transmitters within a
distance (1+)r of the receiver
Interference constraint a single half-duplex
transceiver at each node
Radio interface constraint
T
b
nWTbh
1 2)(
21
)(
1
2 16)(
WTr
T
b
bh
h
hb
receiver
sender
r(1+)r
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Capacity Bound
n
ii
n
ii xnx
1
2
2
1
Note:
Let L be the average (direct-line) distance for all T end-to-end bits.
T
b
bh
h
hbrTL
1
)(
1
T
b
bh
h
hb
T
b
T
b
bh
h
hb rbhrTL
1
)(
1
2
11
)(
1
)()(
nWTWTWTn
TL
816
2 2
nW
L
8
Discussion: what does the result mean?
T
b
nWTbh
1 2)(
21
)(
1
2 16)(
WTr
T
b
bh
h
hb
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Discussion
L depends on traffic pattern (who needs to talk to whom) and positions of the end-to-end (application-level)
senders and (application-level) receivers If end-to-end senders and receivers are
spread out throughout the network, L is large per node capacity
Otherwise, L will be small as network becomes denser
n
1
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Achieving Capacity: Example
n/2 senders and receivers:
L=
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Results: Arbitrary Networks
Protocol Model
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Outline
Admin Wireless mesh capacity
setting arbitrary networks: place nodes optimally to
derive overall upper bound random networks: uniform distribution of
nodes and senders/receivers
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Uniform Random Networks
Uniform distribution of n nodes
n origin-destination (OD) pairs
Each node chooses same power level P, and thus equal radius r(n)
Equal throughput (n) bits/sec for all OD pairs
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Random Networks: Required Bits
Assume: average length of each OD pair is L
Average number of hops:
Total required bit transmissions per second to support (n) :
)(nr
L
)()(nr
Lnn
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Random Networks: Offered Bits
Required bit transmissions per second:
What is the maximum number of transmissions (of bits) in one second? space used per transmission (interference limited):
• at least ¼ r(n)/2]2 = 2r2(n)/16
number of simultaneous transmissions at most (interference limited):
total bits per second
)()(nr
Lnn
2222 )(
16
16/)(
1
nrnr
22 )(
16
nr
W
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Random Networks: Capacity
Required ≤ offered
22 )(
16
)()(
nr
W
nr
Lnn
)(
16)(
2 nnr
WLn
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Connectivity Constraint
Need routes between origin-destination pairs - places a lower bound on transmit range r(n)
Not connected Connected
AD A
D
To maintain connectivity with a high probability, requires r(n) on the order: n
nlog
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Random Networks: Capacity
Required ≤ offered
nn
Lnlog
1)(
22 )(
16
)()(
nr
W
nr
Lnn
)(
16)(
2 nnr
WLn
n
nnr
log)(
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Measurement
Measured scaling law: throughput declines worse with n than theoretically predicted: 1/n1.68
Remaining story line wireless mesh
networks may have low scalability, and need techniques to increase capacity
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Improving Wireless Mesh Capacity
transmission successful if there
are no other transmitters within a
distance (1+)r of the receiver
Interference constraint a single half-duplex
transceiver at each node
Radio interface constraint
T
b
nWTbh
1 2)(
21
)(
1
2 16)(
WTr
T
b
bh
h
hb
nW
L
8
rate*distance capacity:
Reduce LIncrease
W
Approx.optimal
Multipletransceivers
Reduceinterf. area
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Outline
Admin. and recap Wireless mesh network capacity Maximize mesh capacity
Reduce L
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Change Traffic Pattern: Reduce L
Reduce L => make communications local node placement: change the demand patterns (thus
L)• e.g. base stations/access points with high-speed
backhaul
FEA
B C D
BS1 BS2
S
T
infrastructure
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Change Traffic Pattern: Reduce L
Reduce L => make communications local by being patient and wait in a mobile network
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Outline
Admin. and recap Wireless mesh network capacity Maximize mesh capacity
Reduce L Reduce interference
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Reduce Interference Footprint
Antenna design: steered/switched directional antennas
A
D
CB A B
D
C
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Backup Slides
55
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802.11g Overlapping-Channel Collision
Bob
APa on channel Ca
Collision!
Alice
APb on channel Cb
Collision!
Chuck
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802.11g Overlapping-Channel Collision
Bob
APa on channel Ca
More Collision!
Alice
APb on channel Cb
More Collision!
Chuck
Retransmission
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5858
Remap Basic Idea: Structured Permutation
Subcarrier Group
G1 G2 G3 G4
A1 A2 A3 A4Mapping π1
A4 A3 A2 A1Mapping π2
A2 A1 A4 A3Mapping π3
A3 A4 A1 A2Mapping π4
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How Permutation Helps Non-matching collisions on adjacent
channels C1 and C2Subcarrier Group
G1 G2 G3 G4
A1 A2 A3 A41st transmission
2nd transmission A4 A3 A2 A1
A2 A1 A4 A33rd transmission
A3 A4 A1 A24th transmission
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6060
How Permutation Helps (cont’d) Non-matching collisions on non-adjacent
channels C1 and C3
Subcarrier Group
G1 G2 G3 G4
A1 A2 A3 A41st transmission
2nd transmission A4 A3 A2 A1
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Remap Basic Idea: Matching-collision setting
Collision!
Alice Bob
Collision!
APa on channel Ca
APb on channel Cb
Matching collisions on adjacent channels
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Remap for Matching Collisions collisions at adjacent channels C1 and C2 : a time
and frequency view
Pb
∆1∆2
A1 A2
A3
A4
S1 S2Sn
Time
Freq
Pa
B5
B2
B3
B4
A4 A3
A2
A1
S1 S2Sn
B2
B5
B4
B3
P′b
P′a
G1
G3
G2
G5
G4
G2
1
59
13
410
14
3
711
2
68
12