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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 1/24 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 2/24 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! 3/24 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 4/24 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 5/24 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 6/24 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) 7/24 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) 8/24 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 9/24 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}. 10/24 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 11/24 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 ] . 12/24 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. 13/24 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}. 14/24 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 15/24 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. 16/24 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 17/24 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 18/24 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 19/24 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. 20/24 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 21/24 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 22/24 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. 23/24 Interference-Aware MAC Protocol by a Game-Theoretic Approach Q&A Questions or Comments? http://www.stanford.edu/∼abbado Email: [email protected] Thank you! 24/24