1. Reasoning about Performance in Competition and Cooperation
David Tse
Wireless Foundations
Dept. of EECS
U.C. Berkeley
Microsoft Cognitive Radio Summit
June 5, 2008
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2. Competition and Cooperation
Cognitive radios:
compete for resources to transmit their own information
cooperate with each other to improve performance
Basic questions:
What exactly is the resource being competed for?
What exactly is the value-added of a cooperating radio?

3. Reasoning about Performance
How does an information theorist go about it?
formulate a (physical-layer) channel model
compute capacity
identify key dependency on channel parameters

4. Standard PHY-Layer Models
Competition
(interference channel)
Cooperation
(relay channel)
Capture key properties of wireless medium:
Signal strength
Broadcast
Superposition
Unlike p2p capacity, capacity of these networks open for 30 years

5. New Approach Simplify model.
Reason about performance on simplified model,
Approximate optimal performance on original model.
Determination of capacity of interference and relay
channels to within 1 bit/s/Hz.
(Etkin,T. & Wang 06, Avestimehr, Diggavi & T. 07)
In the process, we obtained an interesting abstraction of the PHY layer.

6. Capturing Signal Strength
PHY-layer model Transmit a real number If we have
Abstraction
n / SNR on the dB scale
Least significant bits are truncated at noise level.
Matches approx:

7. Broadcast and Superposition
MSB’s of weak users collide
with LSB’s of strong user.

8. Competition PHY-layer model Abstraction Key coupling parameter:
In symmetric case, channel
described by two parameters:
SNR = signal-to-noise ratio
INR = interference-to-noise ratio
Key coupling parameter:

9. Capacity as a Function of Coupling1
frequency-division
1/2

10. Cooperation
Abstraction
PHY-Layer Model
nSR
nRD x x
nSD

11. Max-Flow Min-Cut Theorem for General Networks
where
Generalization of Ford-Fulkerson Theorem for wireline
networks.

12. Reasoning about Performance via Abstraction
PHY layer higher layers
simple abstraction
of channel