Link Layer:Wireless Mesh Networks

Capacity

Y. Richard Yang

11/13/2012

2

Outline

Admin. and recap Wireless mesh network capacity Maximize mesh capacity

Admin.

Exam Average (mean): 68.6; max = 74

Project check point 1 Sending email to cs434ta@cs.yale.edu Includes contents on

• references• setting

3

4

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

5

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

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

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

}

11

∆1 ≠∆2

11

∆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

}

∆211

2222∆1

How Does ZigZag Work?

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

}

∆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

}

∆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

}

∆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

}

∆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

}

∆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

}

Implementation

• USRP Hardware• GNURadio software• Carrier Freq: 2.4-2.48GHz• BPSK modulation

USRPsTestbed

• 10% HT,

• 10% partial HT,

• 80% perfectly sense each other

802.11a

Throughput Comparison

802.11

Throughput

CD

F o

f co

ncur

rent

flo

w p

airs

Hidden Terminals

Partial Hidden Terminals

Perfectly Sense

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

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

20

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

21

Infrastructure Mode Wireless

APAP

AP wired networkAP: Access Point

Problems of infrastructure mode wireless networks?

802.11 by default operates in infrastructure mode.

22

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

23

Outline

Admin. and recap Wireless mesh network capacity

24

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

25

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

26

Model

Domain is a disk of unit areaThere are n nodes in the domainThe transmission rate is W bits/sec

27

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

Outline

Admin Wireless mesh network capacity

setting arbitrary networks: place nodes optimally to

derive overall upper bound

28

29

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

30

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

31

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

32

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’

33

Area Constraint

For each transmissionwith distance r from sender to receiver, we draw a circle with radius ½ r

These circlesdo not overlap

34

Area Constraint: Global Picture

2

35

Area Constraint: Global Picture

sum over all circles, since each circle has at least ¼ of its area in the unit disk,

2

36

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

37

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

38

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

39

Achieving Capacity: Example

n/2 senders and receivers:

L=

40

Results: Arbitrary Networks

Protocol Model

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

41

42

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

43

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

44

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

45

Random Networks: Capacity

Required ≤ offered

22 )(

16

)()(

nr

W

nr

Lnn

)(

16)(

2 nnr

WLn

46

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

47

Random Networks: Capacity

Required ≤ offered

nn

Lnlog

1)(

22 )(

16

)()(

nr

W

nr

Lnn

)(

16)(

2 nnr

WLn

n

nnr

log)(

48

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

49

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

50

Outline

Admin. and recap Wireless mesh network capacity Maximize mesh capacity

Reduce L

51

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

52

Change Traffic Pattern: Reduce L

Reduce L => make communications local by being patient and wait in a mobile network

53

Outline

Admin. and recap Wireless mesh network capacity Maximize mesh capacity

Reduce L Reduce interference

54

Reduce Interference Footprint

Antenna design: steered/switched directional antennas

A

D

CB A B

D

C

Backup Slides

55

56

802.11g Overlapping-Channel Collision

Bob

APa on channel Ca

Collision!

Alice

APb on channel Cb

Collision!

Chuck

57

802.11g Overlapping-Channel Collision

Bob

APa on channel Ca

More Collision!

Alice

APb on channel Cb

More Collision!

Chuck

Retransmission

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

59

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

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

61

Remap Basic Idea: Matching-collision setting

Collision!

Alice Bob

Collision!

APa on channel Ca

APb on channel Cb

Matching collisions on adjacent channels

62

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