The Fundamental Role of Hop Distance in IEEE 80 The Fundamental Role of Hop Distance in IEEE 80.11 Multi-Hop Ad Hoc Networks IEEE ICNP 2005 Authors: Yan Gao, Dah-Ming Chiu and John C.S. Lui [1]: Offered Load Control in IEEE 802.11 Multi-Hop Ad-Hoc Networks, MASS’04 Ping Chung Ng and Soung Chang Liew The Chinese University of Hong Kong April 12, 2006 Chunyu Hu, University of Illinois at Urbana-Champaign

Chunyu Hu, University of Illinois at Urbana-Champaign Motivation How to maximize throughput of a multi-hop flow? Study the factor: Hop distance (the link length) Problem considered: Hidden terminals Exposed terminals and Signal capture Collisions caused by contention ignored! Exemplary scenario: Chain topology (one-dimension) April 12, 2006 Chunyu Hu, University of Illinois at Urbana-Champaign

Chunyu Hu, University of Illinois at Urbana-Champaign Outline Hidden terminal problem revisited Physical hidden nodes Protocol hidden nodes Signal capture Effect on throughput Analysis of one-dimension network Collision probability Derive a fixed point equation Discussion – why hop distance is important? Conclusion April 12, 2006 Chunyu Hu, University of Illinois at Urbana-Champaign

Hidden Terminal Problem Revisited Rcs Physical hidden nodes: 1->2 Ri 1 2 Rtx Rtx Protocol hidden nodes: 5->6 3 4 d 5 6 Rtx: transmission range Ri: interference range Signal transmitted in this range But outside of Rtx will corrupt the signal received by node 4 Assume loss factor = 4, Ri = 1.78d Rcs: Sensing range April 12, 2006 Chunyu Hu, University of Illinois at Urbana-Champaign

Chunyu Hu, University of Illinois at Urbana-Champaign Rcs Ri 3 4 d Rtx 1 2 5 6 Timeline Comment: Does this problem really exist? Hint: Check the implementation of the interference model in ns2. 5 6 3 4 1 2 April 12, 2006 Chunyu Hu, University of Illinois at Urbana-Champaign

Chunyu Hu, University of Illinois at Urbana-Champaign Signal Capture Focused scenario: Both node 4 and node 7 have packets to transmit. Assume capture threshold CPThresh = 10 and path loss factor = 4. At receiver node 5: SNR = P4/P7 = (2d/d)^4 =16 > 10 However, due to signal capture, if the transmission 7->8 starts first, then node 5 will experience a collision! (Q: why node 5 captures on a signal with strength below RXThresh? ) April 12, 2006 Chunyu Hu, University of Illinois at Urbana-Champaign

Chunyu Hu, University of Illinois at Urbana-Champaign Effect on Throughput Notations: [0, Time] – time interval considered (long duration) Si – the airtime within [0, Time] that node i transmits in “steady-state” Includes DATA + SIFS + ACK + DIFS + retransmission time Not include backoff time slots x – Si/Time  – the collision probability experienced by a transmission Assumptions: Ignore collisions caused by contention and exposed terminal problems. That is, only consider collisions caused by the hidden nodes. April 12, 2006 Chunyu Hu, University of Illinois at Urbana-Champaign

Vulnerable Period induced by Hidden Nodes The hidden terminal problem occurs when The transmission of nodes 4 and 7 overlaps, and The transmission of node 7 starts first. Note: S4, S5 and S6 are non-overlapping S5, S6 and S7 are non-overlapping Node 5 and 6 use together 2x percentage of time in [0, Time] The remaining time in [0, Time] that S4 and S7 may overlap is 1-2x Node 7 uses x transmission time in [0, Time] The vulnerable period induced by node 7 on node 4 is therefore: a = DATA / (DIFS+DATA+SIFS+ACK) Collision prob.  April 12, 2006 Chunyu Hu, University of Illinois at Urbana-Champaign

Chunyu Hu, University of Illinois at Urbana-Champaign Outline Hidden terminal problem revisited Physical hidden nodes Protocol hidden nodes Signal capture Effect on throughput Analysis of one-dimension network Collision probability Derive a fixed point equation Discussion – why hop distance is important? Conclusion April 12, 2006 Chunyu Hu, University of Illinois at Urbana-Champaign

Analysis of One-Dimension Network Consider one-dimension network with arbitrary node density Analysis flow path Derive the collision probability  = ƒ (x) Relate  and hence x to the attempt prob. Pt Already know Pt = G() Solve the fixed point equation April 12, 2006 Chunyu Hu, University of Illinois at Urbana-Champaign

The One-Dimension Network Notations:  – node density, uniquely characterize the network Rcs – sensing range (neighborhood size n = 2Rcs) npr – # of nodes that may cause protocol hidden node problem in the neighborhood of a node nph – # of nodes that may cause physical hidden node problem in the neighborhood of a node d – distance between transmitter and receiver In general, we have: Denote the interfered link by (SI, RI). The protocol hidden nodes are located beyond Rcs of node SI and the interference range of node RI, but within node RI’s interference range. They transmit earlier than SI to cause problems. The physical hidden nodes are located beyond Rcs of node SI, but within the interference range of RI. They transmit later than SI to cause problems. April 12, 2006 Chunyu Hu, University of Illinois at Urbana-Champaign

Derive Collision Probability  Key idea Express the overlapped time between certain nodes based on topological information (that is, ) A generalization of the simple case Redefine the distance in terms of n (the neighborhood size) Any two nodes more than (n-1)/2 apart cannot hear each other and may have overlapped tx time Cnk – the overlapped airtime of two nodes whose distance is (n-1)/2 + k apart. April 12, 2006 Chunyu Hu, University of Illinois at Urbana-Champaign

Overlapped Airtime Cnk For k=1, For k=2, In general, April 12, 2006 Chunyu Hu, University of Illinois at Urbana-Champaign

Derive Collision Probability  (cont’d) There are (n-(n-1)/2-k) node pairs that have Cnk as overlapped airtime. The collision probability caused by Cnk: By induction, it can be shown: and hence The overall collision probability April 12, 2006 Chunyu Hu, University of Illinois at Urbana-Champaign

Chunyu Hu, University of Illinois at Urbana-Champaign Outline Hidden terminal problem revisited Physical hidden nodes Protocol hidden nodes Signal capture Effect on throughput Analysis of one-dimension network Collision probability Derive a fixed point equation Discussion – why hop distance is important? Conclusion April 12, 2006 Chunyu Hu, University of Illinois at Urbana-Champaign

Derive A Fixed Point Equation Step 1. Derive  = ƒ (x) (done) Step 2. x = Pt * T / , where T=DIFS+DATA+SIFS+ACK,  = slot time. Step 3. Pt = Pidle * G(), G() is given in the previous presentation. Step 4: Express Pidle in terms of x: Step 5: Obtain the fixed point equation: April 12, 2006 Chunyu Hu, University of Illinois at Urbana-Champaign

Chunyu Hu, University of Illinois at Urbana-Champaign Derive the Throughput Solve the above fixed-point equation, we can obtain x, and so  and Pt. Throughput: Where Pt is the attempt probability, T/ is the packet transmission time in slots,  is the collision probability, D is effective tx time, = DATA/T, data_rate is the data rate, e.g. 11Mbps. April 12, 2006 Chunyu Hu, University of Illinois at Urbana-Champaign

Chunyu Hu, University of Illinois at Urbana-Champaign Discussions In single-flow networks, only one protocol hidden node is involved regardless of the hop distance and no physical hidden nodes In two-source string network (See the figure above), the optimal distance is the threshold beyond which physical hidden node problem appears. Before a physical hidden nodes joins, the advantage of increasing hop distance dominates the disadvantage Afterwards, the hidden node cause overall degradation April 12, 2006 Chunyu Hu, University of Illinois at Urbana-Champaign

Simulation Validation Single source Two-source April 12, 2006 Chunyu Hu, University of Illinois at Urbana-Champaign

Chunyu Hu, University of Illinois at Urbana-Champaign Conclusion Analyze the throughput in a one-dimension network with arbitrary density Consider the protocol hidden node problem Do not consider the physical hidden node problem Because it doesn’t exist in single-source flows Optimal hop distance is the distance beyond which the physical hidden node problem occurs That means, only occurs in multi-source flows How the physical hidden node problem affects the throughput? April 12, 2006 Chunyu Hu, University of Illinois at Urbana-Champaign