capacity of large scale wireless networks with directional antenna and delay constraint

Capacity of Large Scale Wireless Networks Capacity of Large Scale Wireless Networks with Directional Antenna and Delay with Directional Antenna and Delay

ConstraintConstraint

Guanglin Zhang

IWCT, SJTU

26 Sept, 2012INC, CUHK

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OutlineOutline

Background and related works Background and related works

Unicast capacity for static networksUnicast capacity for static networks

System model and definitionSystem model and definition

Main result and sketch of derivationMain result and sketch of derivation

Multicast capacity for VANETsMulticast capacity for VANETs


ConclusionsConclusions

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OutlineOutline








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BackgroundBackground

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“Broadband's take-up has repeatedly been jumpstarted by must-have applications. Napster drove the shift

from dialup to wired broadband. Now Apple's iPhone is playing the same role in triggering explosive growth

in the wireless Web. Unless we miss our guess, this dynamic is about to rudely change the subject from net

neutrality to a shortage of wireless capacity to meet enthusiastic consumer demand …”

[10/14/2009, Wall Street Journal]

A Roadmap of Technology Evolution (Borrowed from Junshan Zhang’s slides) iPhone on sale day


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Tx Rxpoint-to-point (Shannon 48)

C = log2(1+SNR)

Channel Capacity (Gaussian Channel): Known

Rx1

TxRx

Tx 1

Tx 2Rx 2

multiple-access

(Alshwede, Liao 70’s)

broadcast

(Cover, Bergmans 70’s)

Shannon 48

Ahlswede 71

Liao 72

Cover 72

Slides partially borrowed from D. Tse’s talk on Information Theory of Wireless Networks

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Channel Capacity (Gaussian Channel): Unknown

DD

Tx 1

Relay

SS

Tx 2 Rx 2

Rx 1

relay

(Best known achievable region: Han & Kobayashi 81)

(Best known achievable region: El Gamal & Cover 79)

Han & Kobayashi 81

El Gamal & Cover79


Slides partially borrowed from D. Tse’s talk on Information Theory of Wireless Networks

Typical Related WorkTypical Related Work

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Capacity in wireless ad hoc network not scalable In static ad hoc wireless networks with n nodes, the

per-node throughput behaves as Main reason: spatial interference

Significant gap between demand and wireless capacity

ground breakingground breaking

workwork

[1] P. Gupta, P.R. Kumar, The capacity of wireless networks, IEEE Trans. on Information Theory,

March 2000.

pessimistic pessimistic

resultresult

1

logn n

Typical Related WorkTypical Related WorkMobility can increase the capacity:

Store-carry-forward communication

schemeDrawback: large delays

[2] M. Grossglauser and D. Tse, Mobility Increases the Capacity of Ad Hoc Wireless Networks,

IEEE/ACM Trans. on Networking, August 2002.

1

S DR

8

Typical Related WorkTypical Related Work

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Infrastructure can increase capacity In static ad hoc network with n wireless nodes and k

base stations, the per-node capacity is Assume that base stations are wired together with

unlimited bandwidth, and

Many techniques to increase capacityDirectional antenna, Network coding, MIMO,…

)/( nk

)(),( nOknk

[3]Liu, B. and Liu, Z. and Towsley, D., On the capacity of hybrid wireless networks, INFOCOM 2003.

Difficulty on Network Capacity AnalysisA large number of potential wireless

transmissionsNeighboring transmissions interfere with each

otherDynamic of network topology due to node

mobilityUncertainty of channel quality, e.g., shadowing,

pass loss, multi-path…

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OutlineOutline








System Models and DefinitionSystem Models and DefinitionAssumptions

n nodes and m base stations n nodes randomly placed m base stations regularly

deployed Random source destination

pairs Base stations are relays

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Directional Antenna Every node equipped with

directional antenna Transmitting and receiving

range are common Beam-width:

System Models and Definition(Cont’)System Models and Definition(Cont’)Interference Model

Receiver-based Interference

model

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Delay Constraint Ad hoc mode transmission Infrastructure mode transmission Maximum hops form source to

destination: L No interference between ad hoc

and infrastructure mode transmission

Xk Xl

Xi

Xj

Asymptotic CapacityAsymptotic Capacity

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We say that the per-node capacity is if there exist two constants c and c’ such that

Sustainable: there exists a spatial and temporal scheduling scheme that can achieve such a rate.

Delay: The hops it takes to send packets from source nodes to their destinations.

))(( n

1}esustainablis)(Pr{lim ncn 1}esustainablis)('Pr{lim ncn

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OutlineOutline








Main contribution: the capacity Main contribution: the capacity of unicast network of unicast network

Propose an L-maximum-hop delay constraint strategy, and give the closed-form upper bound of the capacity

Provide the transmission schedule strategy and the routing construction to achieve the upper bound of the capacity

Analyze the relations between throughput capacity and system parameters

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Main ResultsMain Results

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Main theorem : Under the L-maximum-hop resource allocation strategy, by using directional antenna, the throughput capacity of the network is

Proof: sketch

Infrastructure Mode

Capacity

Hybrid

Capacity

Ad Hoc Mode

Capacity

Lower

Bound

Upper

Bound

Lower Bound: Sketch of derivation Lower Bound: Sketch of derivation Construct Voronoi Tessellation

Choose points , …, Spanning

Adjacent Voronoi Cells Cells have common points

Interfering Neighbors Distance between cell

: transmission range : guard zone

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1v 2v nv

(2 ) ( )r n ( )r n

1 2, , nV V V

Lower Bound: Sketch of derivation (Cont’)Lower Bound: Sketch of derivation (Cont’)Number of interfering neighbors

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Remark: every cell has no more

than interfering neighbors,

where

Remark: every cell has no more

than interfering neighbors,

where

1c2 2

1 ( (1 ) )c O

Lower Bound: Routing and SchedulingLower Bound: Routing and SchedulingScheduling

TDMARouting

Random chosen destination

Multihop transmission

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Remark: The scheduling strategy and routing are designed to avoid hot point

Lower Bound: Routing and Scheduling Lower Bound: Routing and Scheduling Traffic load

Expectation of traffic load

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iL

1

2

3log 2 22 2 2

672log

22 3

3

log2

4

log

nk L

nn

kn

c L nc xdx

x n

nc L

n

P(the that cross V and can be used to forward packet)

E(the number of lines in that cross V and can be used to

forward packet)

1

n

i iL

22 3

3

log nc L

n

Lower Bound: Ad Hoc Mode TransmissionLower Bound: Ad Hoc Mode Transmission

When , there exists a constant

, such that

22

1/3

4/3 2/3log

nL

n

0c

When , we have 1/3

4/3 2/3log

nL o

n

Upper Bound: Ad Hoc Mode TransmissionUpper Bound: Ad Hoc Mode Transmission

When , the upper bound of per-node

throughput capacity is

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1/3

4/3 2/3log

nL

n

When , we have the upper bound

per-node throughput capacity

1/3

4/3 2/3log

nL o

n

Remark: the number of simultaneous transmissions for the whole network

is no more than

Capacity Scaling LawsCapacity Scaling Laws

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Multicast Throughput Capacity in Hybrid Wireless Networks

Capacity with respect to L and mCapacity with respect to L and m

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Relations with delay constraint L Relations with number of base stations m

Capacity with respect to Capacity with respect to

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Relations with directional antenna when Relations with directional antenna when

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OutlineOutline








System Model and AssumptionSystem Model and AssumptionAssumption

There are n vehicular nodes and m

base stations in the network At each time slot, n nodes are randomly

and uniformly deployed m base stations are placed regularly There are k multicast sessions

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Directional antenna

Delay constraint Each transmission should be finished

within D time slots

System Model and AssumptionSystem Model and AssumptionMobility model

2D i.i.d. fast mobility model 2D i.i.d. slow mobility model 1D i.i.d. fast mobility model 1D i.i.d. slow mobility model

• Fit the vehicular mobility

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Time scale of mobility Fast mobility

The mobility of nodes is at the

same time scale as the trans-

mission of packets Slow mobility

The mobility of nodes is much slower than the transmission of packets

Main Contribution for Multicast VANETMain Contribution for Multicast VANET

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We present an asymptotic study of the multicast capacity for the hybrid VANETs, and obtain the closed form formula of the multicast capacity in order of magnitude

We analyze the impact of two mobility models and two mobility time scales on multicast capacity of the VANET, which is not considered in the state-of-the-art research, especially under delay constraint

We analyze the impact of the base stations, the beamwidth of the directional antenna, and delay constraint on the multicast capacity

Intuitive Analysis: Multicast CapacityIntuitive Analysis: Multicast Capacity

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Reliable broadcasting channel

12

1 s

W

L n

Unreliable relay channel

Reliable receiving channel

1 12

2

( 1)

ss

W W p

n pL n p

212

21D L n

L

212

21D L n

L

Base station Upper bound

capacity of

hybrid VANET

Directional

trans-ceiving

Main Theorem and Proof IntuitionMain Theorem and Proof Intuition

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2D i.i.d. fast mobility model

Proof: (sketch)

Infrastructure

mode

transmission

2-D i.i.d. fast

mobility model

the packets

have to be

transmitted from

relays to their

destinations

Upper

bound

capacity

the packets are

directly transmitted

from source to their

destinations

2-D i.i.d. fast

mobility model

Infrastructure

mode

transmission

Theorem 1: Under the 2D-i.i.d. fast mobility model and delay constraint D, we have the multicast capacity of ad hoc mode transmission


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2D i.i.d. slow mobility model

The mobile speed of nodes are

much slower than the data

transmission

The mobile speed of nodes are

much slower than the data

transmission

2D i.i.d. slow

mobility model

Throughput

capacity of

VANET

Proof: (sketch)

Theorem 2: Under the 2D-i.i.d. slow mobility model and delay constraint D, we have the number of bits that are successfully delivered to their destinations in T time slots


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1D i.i.d. fast mobility model

Proof: (sketch)

Lemma 8: Under the 1D-i.i.d. fast mobility model and delay constraint D, we have the number of bits that are successfully delivered to their destinations in T time slots

H(B) denotes the minimum distance between the relays that carrying bit B and any of the p destinations.


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1D i.i.d. slow mobility model

Proof: (sketch)

Theorem 3: Under the 1D-i.i.d. slow mobility model and delay constraint D, we have the number of bits that are successfully delivered to their destinations in T time slots

Step 1: Bits transmitted

directly from source to

destinations

By the Cauchy-Schwarz inequality,

Proof SketchProof Sketch

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Meanwhile, we can have, By the Jansen inequality,

Then, we have,

Proof SketchProof Sketch

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Using similar approach as in step 1, we have,Step 2: Bits transmitted from

relay to destinations

Step 3: Bits that are

successfully delivered to

destinations up to time T

Main Result:Main Result:

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2D i.i.d. fast mobility model： 2D i.i.d. slow mobility model：

1D i.i.d. fast mobility model： 1D i.i.d. slow mobility model：

Capacity Scaling LawsCapacity Scaling Laws

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Multicast Throughput Capacity in Hybrid VANET with Directional Antenna and Delay Constraint


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• We study the unicast capacity of large scale wireless networks with directional antenna and delay constraint while the nodes are static.

• The multicast capacity of VANET with different mobility models are investigated and the closed-form formulae are given in order of magnitude.

• We analyze the impact of system parameters on the capacity scaling laws and provide scheduling strategy and routing construction to achieve the capacity bound.

Future WorkFuture Work

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• The capacity of large scale wireless networks with network coding

• The capacity of heterogeneous network with delay constraint

• The capacity of wireless networks with social relationship

• Information theoretic capacity of large scale wireless network

Thank You ！

capacity of large scale wireless networks with directional antenna and delay constraint

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