Download Interference-Aware MAC Protocol for Wireless Networks by a Game

Interference-Aware MAC Protocol by a Game-Theoretic Approach
Interference-Aware MAC Protocol
for Wireless Networks
by a Game-Theoretic Approach
HyungJune Lee, Hyukjoon Kwon,
Arik Motskin, and Leonidas Guibas
Stanford University
IEEE INFOCOM’09, April 23
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Interference-Aware MAC Protocol by a Game-Theoretic Approach
Introduction
Introduction
As wireless networks have been widely deployed, even
small wireless devices can cause strong interference
802.11x, 802.15.4 ZigBee, Bluetooth, 802.16 WiMAX
share the ISM band in the 2.45 GHz range.
Competitive channel usage causes severe volatility in
wireless links.
Poor packet delivery [Souryal07, Lee07]
Traditional Medium Access Control (MAC) to avoid packet
collision
Slotted ALOHA [Roberts75]
CSMA (Carrier Sense Multiple Access) [Kleinrock75]
TDMA (Time Division Multiple Access) [Nelson85]
Mainly to manage intra-cluster interference
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Interference-Aware MAC Protocol by a Game-Theoretic Approach
Introduction
Introduction
Recent experimental studies [Jardosh05, Ergin07] on
inter-cluster interference
Increasing # of APs from 1 to 4 degrades system
throughput by about 50%
Inter-cluster interference causes
a significant performance degradation!
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Interference-Aware MAC Protocol by a Game-Theoretic Approach
Introduction
Introduction
How can we manage the inter-cluster interference?
A centralized inter-cluster interference coordination
scheme?
All the coordinations among APs are hard in practice
Coordination cost could be huge
Network system cannot easily protect from user deviation
Malicious users always use the channel whereas others
starve [Raya04]
Game-theoretic approach characterizes points where a selfish
user cannot benefit by unilateral deviation
resilient to deviation and ensuring robustness
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Interference-Aware MAC Protocol by a Game-Theoretic Approach
Introduction
Main Contributions
Key advantage of studying MAC protocol by game-theoretic
approach
reduce the communication/coordination overhead
between nodes and their home APs
between neighboring APs
lightweght and distributed manner
We propose a distributed binary transmission strategy,
i.e., Transmit or Backoff in uplink scheduling
under inter-cluster interference, allowing concurrent
transmission of nodes from nearby APs,
incorporating more realistic communication model, SINR
model
Static model and Dynamic model
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Interference-Aware MAC Protocol by a Game-Theoretic Approach
Introduction
Related Work
Channel access game from three different categories
NE-based backoff time adaptation [Konorski06, Lee06]
NE-based power control [Wang06, Adlakha07]
NE-based transmission schemes on channel conditions
[Qin03, Hwang06, Cho08] with following assumptions
a collision occurs when two or more users transmit packets
in the same slot
each user’s SNR is i.i.d. Rayleigh fading
However, to consider the inter-cluster interference,
the assumptions are no longer valid
because the SNR is not i.i.d., but depends on # of nodes
concurrently transmitting
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Interference-Aware MAC Protocol by a Game-Theoretic Approach
Problem Formulation
Channel Access Model
Problem Formulation
Channel access model in multiple APs
AP1
AP2
α21h3 α12h2
h2
Tx 1
h3
Tx 2
Tx 3
Tx 4
Figure: Gaussian interference channel model
hi : channel gain between node i and its home AP,
αmn : crosstalk interference ratio between AP m, n (≈ α)
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Interference-Aware MAC Protocol by a Game-Theoretic Approach
Problem Formulation
Channel Access Model
Problem Formulation
SINR model [Gupta00, Moscibroda06] considers the
interference from concurrently transmitting nodes.
Received SNR at home AP
γi =
α
hi pi
≥ SNRth
2
j∈X hj pj + σ
P
γi : SNR at the home AP from node i
X : set of all the interfering nodes
Transmission power is fixed, i.e., pi = p
Transmission strategy
Transmit if a proposed condition holds
Si (hi ) =
Backoff
otherwise
to maximize (network throughput – transmission cost)
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Interference-Aware MAC Protocol by a Game-Theoretic Approach
Channel Access Game
Modeling Access Game
Modeling Access Game
Definition
Players: There are N players with each player i having
type hi , representing channel gain
Actions: ai = {Transmit, Backoff} for all players
i = 1, . . . , N
Payoff function:
Πi (Backoff, a−i ) = 0,
Πi (Transmit, a−i ) = ri (a−i ) − β
β is the cost of consuming transmission power
a−i is the vector of actions of players other than i
ri (a−i ) is the network throughput
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Interference-Aware MAC Protocol by a Game-Theoretic Approach
Channel Access Game
Modeling Access Game
Modeling Access Game
Definition
ri (h−i ) =


 log(1 +


0
hi
α
P
j∈Xi
hj +σ 2
) if
hi
α
P
j∈Xi
hj +σ 2
≥ SNRth
otherwise
where
Xi = {j 6= i : aj = Transmit}.
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Interference-Aware MAC Protocol by a Game-Theoretic Approach
Channel Access Game
Static Game
Static Game
One-shot, simultaneous-move game
Each transmitter knows # of tentative interferers, N
by feedback from APs’ schedulers
Each transmitter knows its own channel gain by feedback
Each transmitter does not know other interferers’ channel
gains, but only distribution of them
AP1
AP2
α21h3 α12h2
h2
Tx 1
h3
Tx 2
Tx 3
Tx 4
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Interference-Aware MAC Protocol by a Game-Theoretic Approach
Channel Access Game
Static Game
Static Game
Definition
Si (hi ) is a Bayesian Nash Equilibrium if and only if:
Si (hi ) ∈ arg max E [Πi (ai , S−i (h−i ))|hi ]
ai ∈Si
for all hi and for all player i.
Definition
In a Bayesian Nash Equilibrium, player i will play Transmit if
and only if
E [Πi (Transmit, S−i (h−i )) |hi ] ≥ E [Πi (Backoff, S−i (h−i )) |hi ] .
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Interference-Aware MAC Protocol by a Game-Theoretic Approach
Channel Access Game
Static Game
Static Game
Proposition
Any Bayesian Nash Equilibrium is given by a threshold strategy
form as follows.
Transmit if hi ≥ hth,i
Si (hi ) =
Backoff
otherwise
where hth,i is the transmission threshold of player i.
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Interference-Aware MAC Protocol by a Game-Theoretic Approach
Channel Access Game
Static Game
Static Game
Proof
When player i chooses Transmit, the expected payoff is given
by the following expression:
ˆ
˜
E Πi (Transmit, S−i (h−i ))|hi
X
Y `
´
´ Y `
P Sj (hj ) = B
=
P Sj (hj ) = T ·
Xi
S
·P
X̄i ={1,...,N}−{i} j∈Xi
α
P
j∈Xi
“
`
· E log 1 +
X
j∈Xi
where Xi
hj ≤
j∈X̄i
!
hi
hj + σ 2
≥ SNRth | {Sj (hj ) = T , ∀j ∈ Xi }
hi
α
P
j∈Xi
´
hj + σ 2
´”
1 ` hi
− σ2
α SNRth
= {j 6= i : aj = Transmit},
| {Sj (hj ) = T , ∀j ∈ Xi },
−β
and X̄i
= {j 6= i : aj = Backoff}.
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Interference-Aware MAC Protocol by a Game-Theoretic Approach
Channel Access Game
Static Game
Static Game
Proof: Cont’d.
The expected payoff function for Transmit is an
increasing function of hi
The expected payoff function for Backoff is 0.
Any rational player will choose Transmit if and only if
E Πi (Transmit, S−i (h−i ))|hi ≥ 0 ⇐⇒ hi ≥ hth,i
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Interference-Aware MAC Protocol by a Game-Theoretic Approach
Evaluation of Static Game
Nash Equilibrium
Proposed scheme is a Bayesian Nash Equilibrium
A user deviates from the NE point,
the expected payoff starts to get
decreasing.
(where N = 10, α = 0.05, σ = 0.1,
SNRth = 10 dB, β = 1)
Efficiency ratio for payoff: 0.58
Efficiency ratio for throughput: 0.99
User 1
User 2
User 3
0.16
0.14
Expected Payoff
Efficiency ratio measure: ratio of
global objective function of BNE
solution and the globally optimal
solution (e.g., hth = 2.13)
0.2
0.18
0.12
0.1
0.08
0.06
0.04
NE=1.49
0.02
0
0.5
1
1.5
Deviated Threshold of User 1
2
2.5
More aggressive transmission not to
be exploited by other users.
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Interference-Aware MAC Protocol by a Game-Theoretic Approach
Evaluation of Static Game
Nash Equilibrium
Instability of the globally optimal symmetric strategy
If selfish user 1 deviates from the
non-BNE threshold to a smaller
threshold, its expected payoff
increases.
Finally, every user will just consume
transmission power without
successful packet delivery
0.4
hth=2.13
0.3
0.25
0.2
0.15
0.1
0.05
0
Symmetric BNE strategy achieves
both stability and balance among
users.
User 1
User 2
User 3
0.35
Expected Payoff
Any selfish user would deviate from
the designated threshold by
decreasing down to 0
0.5
0.45
1.2
1.4
1.6
1.8
2
2.2
2.4
Deviated Threshold of User 1
2.6
2.8
3
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Interference-Aware MAC Protocol by a Game-Theoretic Approach
Evaluation of Static Game
Nash Equilibrium
Threshold strategy should be adapted depending on
: # of users, crosstalk, ambient noise, SNRth , transmission cost
0.4
0.35
0.3
0.25
0.2
4
5
6
7
8
9
10
Total # of Active Users: N
Transmission Probability: P(h > hth)
0.55
0.45
0.4
0.35
0.3
0.25
0.2
4
5
6
7
8
9
10
Total # of Active Users: N
11
SNRth= 5dB
SNRth=10dB
SNRth=15dB
0.7
0.6
0.5
0.4
0.3
0.2
0.1
11
σ=0.05
σ=0.10
σ=0.15
0.5
0.8
Transmission Probability: P(h > hth)
α=0.05
α=0.07
α=0.1
4
5
6
7
8
9
10
Total # of Active Users: N
0.6
Transmission Probability: P(h > hth)
Transmission Probability: P(h > hth)
0.5
0.45
11
β=0.5
β=1.0
β=2.0
0.5
0.4
0.3
0.2
0.1
4
5
6
7
8
9
10
Total # of Active Users: N
11
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Interference-Aware MAC Protocol by a Game-Theoretic Approach
Dynamic Game
Theorem on Convergence
Dynamic Game
Simple dynamic procedure to find an equilibrium of the static
game
without requiring a node to know # of next scheduled
transmitters in neighboring APs
without knowing the distribution of other interferers’
channel gains
1) In each round, a node is randomly activated, and selects
Transmit or Backoff based on the previous status
2) We will prove that the best response dynamics always
converge to a NE in finite rounds
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Interference-Aware MAC Protocol by a Game-Theoretic Approach
Dynamic Game
Theorem on Convergence
Dynamic Game
Theorem
The best-response dynamics with the uniform activation
sequence converge with probability 1 to a pure strategy NE.
Proof.
Refer to the paper.
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Interference-Aware MAC Protocol by a Game-Theoretic Approach
Dynamic Game
Theorem on Convergence
Iteration bounds until best-response dynamics
converge
Dynamics is guaranteed to converge
Average time to convergence is
polynomial in # of players.
Average Number of Rounds to Convergence
1800
1600
1400
1200
1000
800
600
400
200
0
0
50
100
Number of players
150
200
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Interference-Aware MAC Protocol by a Game-Theoretic Approach
Conclusion and Future Work
Conclusion
Problem: the distributed uplink scheduling under
inter-cluster interference
Solution: a distributed binary transmission strategy,
Transmit or Backoff, incorporating a more realistic
SINR model
Static model
Symmetric BNE strategy achieves both stability and balance
among users, and provides a good approximation to the
globally optimal solution
Dynamic model
Converge to the NE after some iterations
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Interference-Aware MAC Protocol by a Game-Theoretic Approach
Conclusion and Future Work
Future Work
We assumed that the crosstalk interference ratio
αmn ≈ E[αmn ] := α, which is the average crosstalk
interference ratio.
Considering statistical variation on the crosstalk would be
an interesting extension.
Considering more generalized networks, e.g., multi-hop
networks with clustering, would be another interesting
extension.
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Interference-Aware MAC Protocol by a Game-Theoretic Approach
Q&A
Questions or Comments?
http://www.stanford.edu/∼abbado
Email: [email protected]
Thank you!
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