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
1
Motivation

How to maximize throughput of a multi-hop flow?
Study the factor:

Problem considered:


• Hop distance (the link length)
•
•
•
•
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
2
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
3
Hidden Terminal Problem Revisited
Physical hidden nodes:
1->2
2
Rtx
3
d
Rtx
4
1
Ri
Rcs
Rcs
April 12, 2006
Protocol hidden nodes:
5->6
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
Chunyu Hu, University of Illinois at Urbana-Champaign
4
Timeline
2
Rtx
3 d
Comment:
Does this problem really exist?
Hint:
Check the implementation of
the interference model in ns2.
Rtx
4
1
Ri
5
Rcs
Rcs
5
6
4
3
1
April 12, 2006
6
Chunyu Hu, University of Illinois at Urbana-Champaign
2
5
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
6
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
7
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
Collision prob. 
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]
x
The vulnerable period induced by node 7 on node 4 is therefore:  HT 
•
a = DATA / (DIFS+DATA+SIFS+ACK)
April 12, 2006
Chunyu Hu, University of Illinois at Urbana-Champaign
1 2 x
8
a
Outline

Hidden terminal problem revisited

Analysis of one-dimension network

• Physical hidden nodes
• Protocol hidden nodes
• Signal capture
• Effect on throughput
•
•
•
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
9
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
10
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:
April 12, 2006
Chunyu Hu, University of Illinois at Urbana-Champaign
11
Derive Collision Probability 

Key idea
•
•

Redefine the distance in terms of n (the
neighborhood size)
•

Express the overlapped time between certain nodes
based on topological information (that is, )
A generalization of the simple case
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
x

x
n 1
1
x
2
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
Outline

Hidden terminal problem revisited

Analysis of one-dimension network

• Physical hidden nodes
• Protocol hidden nodes
• Signal capture
• Effect on throughput
•
•
•
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
Derive the Throughput


Solve the above fixed-point equation, we can
obtain x, and so  and Pt.
Throughput:
T
  Pt   (1   )  D  data _ rate

Where
April 12, 2006
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.
Chunyu Hu, University of Illinois at Urbana-Champaign
18
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
April 12, 2006

Two-source
Chunyu Hu, University of Illinois at Urbana-Champaign
20
Conclusion

Analyze the throughput in a one-dimension
network with arbitrary density
•
•

• Because it doesn’t exist in single-source flows
Optimal hop distance is the distance beyond
which the physical hidden node problem occurs
•

Consider the protocol hidden node problem
Do not consider the physical hidden node problem
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
21