1. Understanding Radio Irregularity in Wireless Networks Torsten Mütze, ETH Zürich joint work with Patrick Stüdi, Fabian Kuhn and Gustavo Alonso

2. Outline Motivation Network Model Connectivity Interference

3. Motivation Ideal: - circular transmission range Path Loss Model (deterministic) Connectivity? Capacity? More realistic: - obstacles in the transmission path - non-isotropic antennas Log-normal Shadowing Model (randomized)

4. Network Model (1)

5. Network Model (2) Path Loss Model Log-normal Shadowing Model [Hekmat, Mieghem 06; Bettstetter, Hartmann 05; Miorandi, Altman 05; Orriss, Barton 03] Radio irregularity is controlled through a single parameter, the shadowing deviation

6. Connectivity (1) Connectivity: probability of the network graph to be connected Biased Analysis: Connectivity increase is caused by a higher expected node degree (=enlarged radio transmission range) How to do a fair comparison between different levels of radio irregularity? Expected node degree [Bettstetter, Hartmann 05]

7. Connectivity (2) Normalization! When increasing, vary the transmission power p 0 as a function of such that the expected node degree remains constant [Jonasson 01], [Roy, Tanemura 02] Why? Edge length distribution Longer connections help Surprise: Connectivity increases with irregularity, even under constant node degree

8. Interference limits the throughput capacity of a network [Stüdi, Alonso 06] Interference (1) Interferers: smallest set of nodes that must not transmit concurrently to the communication from b to a signal interference + noise threshold Signal-to-interference-plus-noise ratio model (SINR) a b pabpab I interferers non-interferers I

9. Expected number of interferers for fixed p a  b Biased Analysis: Interference increase is caused by a higher cumulated noise Normalization! Keep the expected cumulated noise constant when varying Expected number of interferers for fixed p a  b Interference (2) Expected cumulated noise a Why? Power density function More nodes with small/large transmission power (=more non-interferers) Surprise: Interference decreases with irregularity (under constant expected cumulated noise)

10. Summary Studied impact of log-normal shadowing on connectivity and interference First unbiased analysis: fair comparison between different levels of radio irregularity Beneficial impact of log-normal shadowing on both connectivity and interference (improved connectivity, reduced interference) Existing bounds on connectivity and capacity derived in a circular transmission range model are lower instead of upper bounds

11. Thank you!