1. The Fundamental Role of Hop Distance in IEEE 80
The Fundamental Role of Hop Distance in IEEE 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 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

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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

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

14. 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

15. 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

16. 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

17. 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

18. 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

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

20. 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