A General Model and Analysis of Physical Capture in 802.11 Networks

1. A General Model and Analysis of Physical Capture in 802.11 Networks H. Chang, V. Misra, and D. Rubenstein Computer Science Department Columbia University, NY 10027 Presented by Tae Hyun Kim

2. Contents • Motivation • Network Model • Capture Modeling • System Throughput • Interference Modeling • Iterative Method • Convergence of Method • Simulation • Conclusion • Comments

3. Motivation C A D • Packet capture – one of concurrently transmitted packets can be decoded • Collision doesn’t necessarily corrupt packet • Depend on how severe interference is • How could we describe this into previous analytic model? • Especially when multiple TX-RX pairs exist B One of the simplest networks considered in this paper

4. Motivation (cont.) • Qualnet simulation on capture effect • Note that distance between TX and RX is only 10 m Low rate networkcould benefit capturedue to low SINR requirement High rate networkeasily suffers frominterference

5. Network Model • All nodes are in carrier-sense range • No desynchronized collisions (e.g. ones by hidden nodes) • Nodes are composed of predetermined TX-RX pairs • Distance between TX and RX is less than 10m • No packet losses if not collided • Single hop infinite traffic – to use Bianchi’s

6. Capture Model • System throughput • Interference modeling • Iterative method • Convergence of method

7. System Throughput • Reuse Bianchi’s model • Every node has same behavior pattern • Constant channel access probability, τ • Constant conditional collision probability, p • Modeling as τ -persistent CSMA Access with τ Concurrent transmissions (collision) happen with p τ time time slot Then, the relationship is: n - # of nodes

8. System Throughput (cont.) • Modified model reflects the role of interference • Collision does not necessarily fail all transmissions • p and τdepend on each node’s location Carrier sense area signal interference τ3 τ2 A p3 C a c p1 b p2 B τ1

9. System Throughput (cont.) • pi is redefined as probability that • When a node decides to transmit, • There is at least one more transmitter • AND interference is high enough to corrupt a packet • Packet capture happens • When a node decides to transmit, • There is at least one more transmitter • BUT, interference is tolerable

10. System Throughput (cont.) • Access probability is again, • Next presentation by Yong Yang deals with details to derive this • Linear approximation to reduce computational complexity • α= 0.180820691, β=0.128201376 for 802.11a (Taylor series expansion and first-order approximation)

11. System Throughput (cont.) • Transmission probability of a node set A • One cycle of a transmission • Backoff + transmission time No one transmits At least one node transmits Backoff Transmission Backoff Transmission Backoff

12. System Throughput (cont.) A node set with rjrate • Transmission time • Approximations • When packets collide, ACK does not follow  assumed there is always following ACK # of rates A entire node set ??

13. System Throughput (cont.) • Average number of transmissions • Then, the system throughput is Packet length

14. Interference Modeling • pi has not been modeled yet! • That will include packet capture! • Combinatorial probability of concurrent transmission • Consider nodes except for i • Nodes in J transmit while other nodes shut up • Can be extended to multiple nodes exception

15. Interference Modeling (cont.) • Interference function • Based on active interferer set, J • Decide if a packet can be captured or not • Empirically or via simulation, this can be obtained • Note • f(.) does not need receiver information

16. Interference Modeling (cont.) • Define N’s power set as 2N • Using combinatorial prob. and interference function, • Summing up all possible combinations of interferers • Suffers from computational complexity

17. Iterative Method • Iteration method to efficiently compute pi and τi • Still has O(nn) • Take another approximation to get O(nt) p0i Exponent is iteration index τ1i and T1i(J) p1i τ2i and T2i(J) p2i

18. Convergence of Method • Notations • Recall • Tki,m(J) means that, when we don’t consider nodes i and m, nodes in J interfere while other nodes shut up Exponent is iteration index

19. Convergence of Method (cont.) • Theorem 1 (Monotonicity of maximum difference) • With any initial values pi0 and any interference function fri, each iteration k in the method satisfies the monotonicity of the maximum difference Dk • This is proven if,

20. Convergence of Method (cont.) • Let • For any other node i in the node set N, • Recall again, • Tki,m(J) means that, when we don’t consider nodes i and m, nodes in J interfere while other nodes shut up When node m transmit When node m does not transmit

21. Convergence of Method (cont.) • Then,

22. Convergence of Method (cont.) before going further, • Lemma 4 • Consider node set N and nodesassuming • For any

23. Convergence of Method (cont.) • Using Lemma 4, • This can be rewritten as • Therefore, (Lemma 1 in the paper)

24. Convergence of Method (cont.) • Need to prove the relationship for node m • In order to use the same reasoning, pick up a node n which satisfies, • That is, • Therefore, by the same reasoning, • Theorem I, then, is proved

25. Simulation EIFS is a particularly long IFS to protect immediate ACK • Qualnet modification • Turn off EIFS due to EIFS unfairness problem • Slot synchronization Receiver A keeps receivingcorrupted packet, so it continuesto reset EIFS timer, not participatingMAC contention Backoff timers using nanosecond units must be using integer unit Node B grabs medium!

26. Simulation (cont.) • Setup • 200m x 200m is divided into U squares • U= # of TX-RX pairs, U=9, 25, 49, 64 • Random TX location in each square • K = # of iteration = 10 • Analysis accuracy If actual interferers are morethan t, then errors should be larger

27. Simulation (cont.) • ‘Relatively’ accurate • Recall t is the maximum number of concurrent interferers that the model can account for Error increasesas t is fixed to 3 Less interferers More interferers

28. Conclusion • Presented general capture model • To efficiently compute model’s variables, iteration method is proposed • Convergence of the method is proven • Accuracy is verified via Qualnet simulations

29. Comments • Is the model general? • There MUST be one-to-one TX-RX pairs • All nodes MUST be in carrier sense range • TX-RX MUST be very close to each other • Is the model accurate? • Recall that in Bianchi’s error < 1% • Always ACK follows TX trial • Most essential part is to derive the interference function, which is not dealt with

30. THANK YOU!ANY QUESTIONS?