1. Bridging the Gap: A Deterministic Model for Wireless Links David Tse Wireless Foundations U.C. Berkeley NSF Wireless Networks Workshop Aug 27, 2007 TexPoint fonts used in EMF: AAA A AA A A A A A A A

2. Key Features of Wireless Channels broadcast interference high dynamic range in channel strengths between different nodes Basic PHY layer model- additive Gaussian channel:

3. Gaussian Model: Basis for PHY-Layer Advances Many PHY-layer advances in past decade based on the Gaussian model. Examples: MIMO, interference cancellation, superposition coding Advances in the context of point-to-point, many- to-one, and one-to-many settings. Hard to use to reason about more complex wireless network configurations. Capacity of simple networks with single-relay or two interfering point-to-point links are open problems for eons.

4. Common Channel Models for Wireless Networks 0/1 connectivity models packet collision models SINR based model: treating interference as noise These models do not capture key properties of wireless medium constrains the design of innovative communication schemes

5. Bridging the Gap More research needed in model building. As an example we discuss a deterministic channel model which : captures several key aspects of the wireless medium is scalable to complex wireless networks

6. Point-to-Point Link Rx observes  most-significant bits of the transmitted signal.  is proportional to the SNR on the dB scale.

7. Broadcast user 2 user 1 Users with higher SNR see more bits of the transmitted signal. Implemented by superposition coding at the PHY layer.

8. Multiple Access user 2 user 1 mod addition More significant bits of strong user observed cleanly. Collision with weak user at the less significant bits. Implemented by interference cancellation at the PHY layer.

9. Application to Relay Networks What is the capacity of this network from a single source S to a single destination D?

10. Max-Flow Min-Cut Theorem Theorem: where Generalization of Ford-Fulkerson Theorem for wireline networks.

11. Conclusion PHY layer higher layers simple wireless channel model