capacity of large scale wireless networks with directional antenna and delay constraint
DESCRIPTION
Capacity of Large Scale Wireless Networks with Directional Antenna and Delay Constraint. Guanglin Zhang IWCT, SJTU 26 Sept, 2012 INC, CUHK. Outline. Background and related works Unicast capacity for static networks System model and definition Main result and sketch of derivation - PowerPoint PPT PresentationTRANSCRIPT
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
Main result and sketch of derivationMain result and sketch of derivation
ConclusionsConclusions
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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
Main result and sketch of derivationMain result and sketch of derivation
ConclusionsConclusions
3
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
BackgroundBackground
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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
BackgroundBackground
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
9
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
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
Main result and sketch of derivationMain result and sketch of derivation
ConclusionsConclusions
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
12
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
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
Main result and sketch of derivationMain result and sketch of derivation
ConclusionsConclusions
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
18
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
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
Main result and sketch of derivationMain result and sketch of derivation
ConclusionsConclusions
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
Main Theorem and Proof IntuitionMain Theorem and Proof Intuition
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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
Main Theorem and Proof IntuitionMain Theorem and Proof Intuition
34
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.
Main Theorem and Proof IntuitionMain Theorem and Proof Intuition
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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
ConclusionsConclusions
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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 !