Reasoning about Performance in Competition and Cooperation David Tse Wireless Foundations Dept. of EECS U.C. Berkeley Microsoft Cognitive Radio Summit June 5, 2008 TexPoint fonts used in EMF: AAAAAAAAAAAAAA

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?

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

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

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.

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:

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

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:

Capacity as a Function of Coupling 1 frequency-division 1/2

Cooperation Abstraction PHY-Layer Model nSR nRD x x nSD

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

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