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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: A A A A A A A A A A A A A A. Competition and Cooperation . Cognitive radios:
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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.
PHY-layer model Transmit a real number If we have Capturing Signal Strength Abstraction n /SNR on the dB scale Least significant bits are truncated at noise level. Matches approx:
Broadcast and Superposition Broadcast Superposition MSB’s of weak users collide with LSB’s of strong user.
Competition PHY-layer modelAbstraction 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 Theorem: where Generalization of Ford-Fulkerson Theorem for wireline networks.
Reasoning about Performance via Abstraction PHY layer higher layers simple abstraction of channel