1. CS434/534: Topics in Networked (Networking) Systems Wireless Foundation: Wireless Mesh Networks Yang (Richard) Yang Computer Science Department Yale University 208A Watson

2. Outline Recap Wireless background Frequency domain
Modulation and demodulation
Wireless channels
Wireless PHY design
Wireless MAC design (one hop)
wireless access problem and taxonomy
wireless resource partitioning dimensions
media access protocols
From single-hop MAC to multi-hop mesh
wireless mesh network capacity
maximize mesh capacity

3. Admin. PS2 questions Project first check point
Due Thursday after break

4. Recap: The Hidden Terminal Problem
A is sending to B, but C cannot detect the transmission
Therefore C sends to B
In summary, A is “hidden” from C

5. Recap: 802.11 RTS-CTS-data-ACK
DIFS
RTS
data
10 usec
sender
SIFS
SIFS
CTS
SIFS
ACK
receiver
NAV (RTS)
DIFS
data
other
stations
NAV (CTS) t
defer access
new contention

6. B1 and B2 are backoff intervals
Recap: CSMA/CA
busy
B1 = 25
B2 = 20
B1 = 5
data
wait
data
wait
B2 = 10
B2 = 15
busy
B1 and B2 are backoff intervals
at nodes 1 and 2
cw = 31

7. Recap: PIFS D: downstream poll, or data from point coordinator
SIFS D D
point
coordinator
SIFS U
polled
wireless
stations
NAV
NAV
contention free period t
medium
busy
contention
period
D: downstream poll, or data from point coordinator
U: data from polled wireless station

8. Recap: Wireless Link Access Control
Problem: single shared medium, hence if two transmissions overlap on all dimensions [time, space, frequency, and code], then it is a collision
+CS+CD+EB
Slotted ALOHA
Ethernet
+CA +ACK
+ RTS/CTS
Hidden-terminal Collision detection/ prevention
Zigzag decoding

9. Recap: ZigZag Decoding
Exploits ’s behavior
Retransmissions
Same packets collide again
Senders use random jitters
 Collisions start with interference-free bits Pa Pa
…………
How do we leverage these interference free bits to decode the collisions? ∆1 Pb ∆2 Pb
Interference-free Bits

10. ZigZag Algorithm ∆1 ≠∆2 ∆1 ∆2 1 1
while (exists a chunk that is interference-free in one collision and has interference in the other) {
decode and subtract from the other collision }

11. How Does ZigZag Work? ∆1 ≠∆2 ∆1 ∆2 1 1 2
while (exists a chunk that is interference-free in one collision and has interference in the other) {
decode and subtract from the other collision }

12. How Does ZigZag Work? ∆1 ≠∆2 ∆1 ∆2 1 3 2 2
while (exists a chunk that is interference-free in one collision and has interference in the other) {
decode and subtract from the other collision }

13. How Does ZigZag Work? ∆1 ≠∆2 ∆1 ∆2 1 3 3 2 4
while (exists a chunk that is interference-free in one collision and has interference in the other) {
decode and subtract from the other collision }

14. How Does ZigZag Work? ∆1 ≠∆2 ∆1 ∆2 1 3 5 4 2 4
while (exists a chunk that is interference-free in one collision and has interference in the other) {
decode and subtract from the other collision }

15. How Does ZigZag Work? ∆1 ≠∆2 ∆1 ∆2 1 3 5 5 2 4 6
while (exists a chunk that is interference-free in one collision and has interference in the other) {
decode and subtract from the other collision }

16. How Does ZigZag Work? ∆1 ≠∆2 ∆1 ∆2 1 3 5 7 6 2 4 6
while (exists a chunk that is interference-free in one collision and has interference in the other) {
decode and subtract from the other collision }

17. How Does ZigZag Work? ∆1 ≠∆2 ∆1 ∆2 1 3 5 7 7 2 4 6 8
while (exists a chunk that is interference-free in one collision and has interference in the other) {
decode and subtract from the other collision }
Thus, even in the face of collisions, we are able to correctly receive 2 packets in 2 timeslots.
Delivered 2 packets in 2 timeslots
As efficient as if the packets did not collide

18. Outline Admin. and recap Media access control Slotted Aloha
Hidden terminal
Example:
Hidden terminal with revisited
Overall idea
Technical issues
Collision detection

19. Collision Detection: How does the AP know it is a Collision and Where the Second Packet Starts?
Time ∆

20. Detecting Collisions and the Value of ∆
Time
AP received signal
Correlate
Packets start with known preamble
AP correlates known preamble with signal ∆
Correlation
Time

21. Pa Pb
P’a
P’b
Matching Collision
Question to think offline: Given (P1 + P2()) and (P1’, P2’(’)), how to determine that P1 = P1’ and P2 = P2’
Determine offset first
Correlation of P2() and P2’(’)

22. Outline Admin. and recap Media access control Slotted Aloha
Hidden terminal
Example:
Hidden terminal with revisited
Overall idea
Technical issues
Collision detection
Subtracting chunks

23. How Does the AP Subtract the Signal?1 2
Channel’s attenuation or phase may change between collisions
Can’t simply subtract a chunk across collisions
Alice’s signal in first collision
Alice’s signal in second collision
Now that the AP knows where the second packet starts, it is going to take the interference-free chunk from at the start of the first collision and subtract it from the second.
In practice, it is not that simple…………..

24. Re-modulate bits to get channel-free signal 1 2
Subtracting a Chunk
Decode chunk into bits
Removes effects of channel during first collision
Re-modulate bits to get channel-free signal
Apply effect of channel during second collision
Use correlation to estimate channel despite interference
The solution to this problem however is simple.
……..
Now the AP can subtract the first chunk. The AP iterates this process to decode both the whole packet.

25. What if AP Makes a Mistake?
But, as is the usual case, channel adds noise which could lead to decoding errors.

26. What if AP Makes a Mistake?
Bad News: Errors can propagate 1 3 1 ∆1 ∆2 2 2
For example, if the channel was noisy it can cause a decoding error in chunk 1.
Since we subtract chunks across collisions, errors in the first collision can propagate to the second collision
For example, Now when we subtract, the error in chunk 1 can lead to a decoding mistake in chunk 2, which itself could propagate further.
Can we deal with these errors?

27. What if AP Makes a Mistake?
Good News: Temporal Diversity
A bit is unlikely to be affected by noise in both collisions ∆1 ∆2
The good new is that we have temporal diversity. Each bit appears twice on the channel.
It is unlikely that the same bit is in error in both collisions.
We can leverage this property by decoding each bit twice using two independent decodings.
But how do we get these two independent decodings?
I have already described to u … one way of decoding.
Get two independent decodings

28. AP Decodes Backwards as well as Forwards∆1 ∆2 2 2 3 1 1
Errors propagate differently in the two decodings
Which decoded value should the AP pick?
But in addition to this forward decoding method we can also decode backwards.
For each bit, AP picks the decoding that has a higher PHY confidence

29. Outline Admin. and recap Media access control Slotted Aloha
Hidden terminal
Example:
Hidden terminal with revisited
Overall idea
Technical issues
Collision detection
Subtracting chunks
Deployment

30. Acknowledgement
Use as much synchronous acknowledgement as possible for backward compatibility

31. Implementation USRP Hardware GNURadio software
Carrier Freq: GHz
BPSK modulation

32. Testbed USRPs 802.11a 10% HT, 10% partial HT,
80% perfectly sense each other
Blah blah blah…
Since Software radios do all operations in software in user mode, they cannot perform carrier sense accurately. So, to capture carrier sense, each of our nodes have both and USRP radios. We first run the experiment using the nodes which apply carrier sense. Then we repeat the same experiment the USRP nodes, while forcing them to have the same number of collisions as the corresponding nodes.

33. Throughput Comparison
Perfectly Sense
Partial Hidden Terminals
Hidden Terminals
CDF of concurrent flow pairs
802.11
We see three regions. Some nodes are complete hidden terminals and hardly get any throughput. Others are partial hidden terminals and get sub-optimal throughput, and the rest are get good throughput.
Throughput

34. Throughput Comparison
ZigZag Exploits Capture Effect
Hidden Terminals get high throughput
CDF of concurrent flow pairs
ZigZag
802.11 …
what used to be hidden terminals, they get excellent throughput.
Throughput

35. 3 packets in 2 time slots  better than no collisions
Capture Effect
Subtract Alice and combine Bob’s packet across collisions to correct errors
Pa1
Pa2 ∆1 ∆2 Pb Pb
Finally, ZigZag makes a better use of capture effects.
Capture effect can happen when the AP can decode Alice’s packets despite interference from Bob. But in ZigZag, the AP also subtract Alice’s packets from the collision signals to get Bob’s packets. Since Bob’s signal is so weak it is unlikely that one collision is sufficient to decode it. But ZigZag can combine the results of decoding Bob’s packet across both collisions to improve performance.
3 packets in 2 time slots  better than no collisions

36. May 21, 2007
May 21, 2007
Summary
Basic lesson:
Traditional thinking was on avoiding collisions
Zigzag changed the way of thinking: decoding collisions
Many extensions of the Zigzag idea: decoding collisions, instead of avoiding collisions
See Remap in Backup Slides
A good area for creative thinking 36
Yale University
Yale University 36

37. Infrastructure Mode Wireless
by default operates in infrastructure mode. AP
wired network
AP: Access Point AP AP
Problems of infrastructure mode wireless networks?

38. Mesh Networks ad-hoc (mesh) mode Benefits fast and low-cost deploymentAP
wired network
AP: Access Point AP AP
Benefits
fast and low-cost deployment
no central point of failure
no APs overhead for users who can reach each other
ad-hoc (mesh) mode
Issues?

39. Outline Recap Wireless background Frequency domain
Modulation and demodulation
Wireless channels
Wireless PHY design
Wireless MAC design (one hop)
From single-hop MAC to multi-hop mesh
understanding: wireless mesh network capacity

40. Capacity of Mesh Networks
The question we study:
how much traffic can a mesh wireless network carry, assuming an oracle to avoid the potential overhead of distributed synchronization (MAC)?
Why study capacity?
learn the fundamental limits of mesh wireless networks
separate the spatial reuse perspective and system design perspective
gain insight for designing effective wireless protocols

41. Mesh Transmission Constraints
transmission successful if there are no other transmitters within a distance (1+D)r of the receiver
receiver
sender r
(1+D)r
Interference constraint
a single half-duplex transceiver at each node:
either transmits or receives
transmits to only one receiver
receives from only one sender
Radio interface constraint

42. Model Domain is a disk of unit area There are n nodes in the domain
The transmission rate is W bits/sec

43. Capacity of Mesh Wireless Network
Consider two types of networks
arbitrary networks: place nodes optimally to derive overall upper bound
random network: nodes are placed randomly

44. Outline Recap Wireless background Frequency domain
Modulation and demodulation
Wireless channels
Wireless PHY design
Wireless MAC design (one hop)
From single-hop MAC to multi-hop mesh
understanding: wireless mesh network capacity
setting
arbitrary networks: place nodes optimally to derive overall upper bound

45. Transmission Model: Bit-time Perspective
Chop time into a total of WT bit-times in T seconds
The transmission decision is made for each bit
bit time 1
bit time 2
bit time t
bit time WT 1 2 3 5 4 1 2 3 5 4

46. Transmission Model: End-to-end Perspective
Assume the network sends a total of T end-to-end bits in T seconds
Assume the b-th bit makes a total of h(b) hops from the sender to the receiver
Let rbh denote the hop-length of the h-th hop of the b-th bit 1 2 T 2

47. Hop-Count Constraint 2
Since there are a total of WT bit-times, and during each bit-time there are at most n/2 simultaneous transmissions, we have

48. Area Constraint m k (1+)r’ r’ i j (1+)r r ½ r’ ½ r
Consider two simultaneous transmissions at a bit-time i j
(1+)r r
½ r’
½ r
Djm + r >= Dim >= (1+)r’
Djm + r’ >= Djk >= (1+)r
 Djm >= (r+r’)  /2

49. Area Constraint
For each transmission with distance r from sender to receiver, we draw a circle with radius ½  r
These circles do not overlap

50. Area Constraint: Global Picture2

51. Area Constraint: Global Picture2
sum over all circles, since each circle has at least ¼ of its area in the unit disk,

52. Summary: Two Constraints
Radio interface constraint
Interference constraint
a single half-duplex transceiver at each node
transmission successful if there are no other transmitters within a distance (1+D)r of the receiver
receiver
sender r
(1+D)r

53. Discussion: what does the result mean?
Capacity Bound
Note:
Let L be the average (direct-line) distance for all T end-to-end bits.
Discussion: what does the result mean?

54. Discussion L depends on
traffic pattern (who needs to talk to whom) and
positions of the end-to-end (application-level) senders and (application-level) receivers
If end-to-end senders and receivers are spread out throughout the network, L is large
per node capacity
Otherwise, L will be small as network becomes denser

55. Achieving Capacity: Example
n/2 senders and receivers:
L=

56. Results: Arbitrary Networks
Protocol Model

57. Outline Recap Wireless background Frequency domain
Modulation and demodulation
Wireless channels
Wireless PHY design
Wireless MAC design (one hop)
From single-hop MAC to multi-hop mesh
understanding: wireless mesh network capacity
setting
arbitrary networks: place nodes optimally to derive overall upper bound
random networks: uniform distribution of nodes and senders/receivers

58. Uniform Random Networks
Uniform distribution of n nodes
n origin-destination (OD) pairs
Each node chooses same power level P, and thus equal radius r(n)
Equal throughput (n) bits/sec for all OD pairs

59. Random Networks: Required Bits
Assume: average length of each OD pair is L
Average number of hops:
Total required bit transmissions per second to support l(n) :

60. Random Networks: Offered Bits
Required bit transmissions per second:
What is the maximum number of transmissions (of bits) in one second?
space used per transmission (interference limited):
at least ¼ p [Dr(n)/2]2 = pD2r2(n)/16
number of simultaneous transmissions at most (interference limited):
total bits per second

61. Random Networks: Capacity
Required ≤ offered 

62. Connectivity Constraint
Need routes between origin-destination pairs - places a lower bound on transmit range r(n) A A D D
Connected
Not connected
To maintain connectivity with a high probability, requires r(n) on the order:

63. Random Networks: Capacity
Required ≤ offered 

64. Measurement
Measured scaling law: throughput declines worse with n than theoretically predicted: 1/n1.68
Remaining story line
wireless mesh networks may have low scalability, and need techniques to increase capacity

65. Improving Wireless Mesh Capacity
Reduce interf. area
Radio interface constraint
Interference constraint
a single half-duplex transceiver at each node
transmission successful if there are no other transmitters within a distance (1+D)r of the receiver
Multiple transceivers
Approx. optimal
Reduce L
Increase W
rate*distance capacity: