Understanding Radio Irregularity in Wireless Networks

Torsten Mütze, ETH Zürichjoint work with Patrick Stüdi, Fabian Kuhn and Gustavo Alonso

Outline

Motivation Network Model Connectivity Interference

Motivation

Ideal:- circular transmission rangePath Loss Model (deterministic)

Connectivity?Capacity?

More realistic:- obstacles in the transmission path- non-isotropic antennasLog-normal Shadowing Model (randomized)

50 100 150 200

0.2

0.4

0.6

0.8

1

Network Model (1)

0.5 1 1.5 2

0.2

0.4

0.6

0.8

1

0 10 20 30 40 50

0.00001

0.0001

0.001

0.01

0.1

1

Network Model (2)Path Loss Model

0.5 1 1.5 2

0.2

0.4

0.6

0.8

1

Log-normal Shadowing Model

[Hekmat, Mieghem 06; Bettstetter, Hartmann 05; Miorandi, Altman 05; Orriss, Barton 03]

0 10 20 30 40 50

0.00001

0.0001

0.001

0.01

0.1

1

Radio irregularity is controlled througha single parameter, the shadowing deviation

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]

Connectivity (2)Normalization!When increasing , vary thetransmission power p0 as afunction of such that theexpected node degree remainsconstant

[Jonasson 01], [Roy, Tanemura 02]

Why?Edge length distribution

Longer connections help

Surprise: Connectivity increases withirregularity, even under constant nodedegree

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 + noisethreshold

Signal-to-interference-plus-noise ratio model (SINR)

ab

pab

I interferers

non-interferersI

Expected number of interferers for fixed pab

Biased Analysis: Interference increase is caused by a higher cumulated noiseNormalization! Keep the expected cumulated noise constant when varyingExpected number of interferers for fixed pab

Interference (2)Expected cumulated noise

a

Why?Power density function

More nodes with small/largetransmission power (=more non-interferers)

Surprise: Interference decreases with irregularity (under constant expected cumulated noise)

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

Thank you!