“SDJS: Efficient Statistics in Wireless Networks”

Albert Krohn, Michael Beigl, Sabin Wendhack

TecO (Telecooperation Office)Institut für TelematikUniversität Karlsruhe

www.teco.edu

Albert Krohn, Michael Beigl, Sabin Wendhack, TecO, Universität Karlsruhe

SDJS: research and application area

WSN (wireless sensor network) Battery powered Low computation capabilities

MANET (mobile ad hoc networks) Fast changing environment Devices frequently join and leave a group

BAN (body area network), PAN (personal area networks)

Sensors attached to people Many small devices

Ubiquitous and Pervasive Computing Settings with many devices (typically >100) Battery powered Mid computation capabilities

Albert Krohn, Michael Beigl, Sabin Wendhack, TecO, Universität Karlsruhe

SDJS: Synchronous Distributed Jam Signalling

What is SDJS?

Method for ultra fast estimation of a parameter of a group of devices

Novel transmission scheme Extension of standard wireless ad hoc protocol Synchronous, parallel, superimposing jam signals Works infrastructure less For highly mobile settings with high number of

networked devices

Example for this talk: “How many devices are present in the cell?”

Albert Krohn, Michael Beigl, Sabin Wendhack, TecO, Universität Karlsruhe

Related Work

Example:“How many devices are present in the cell?”

Budianu et al. 2003: Collect IDs from the Devices and do a Good-Turing estimation, can be done iteratively Targeted on large scale networks, not on speed Also probabilistic

Vogt 2002: For passive RFID Using a slotted aloha protocol, where tags randomly select a slot Adaptive frame size Time to estimate 200 nodes with 99% reliability > 3 sec. (assuming ISO 18000 RFID standard)

Normal “ping” on 802.11b: Around 5 seconds (best case) for 100 stations

Albert Krohn, Michael Beigl, Sabin Wendhack, TecO, Universität Karlsruhe

Motivation Idea of SDJS

Example:“How many devices are present in the cell?”

Traditional: Ping & HELO, OLEHSlow, each node answers Packet implosion, collisionsHigh bandwidth necessary“deterministic”Generic functionality of data transport in the networkSame mechanisms for all information flow

Novel:Specific solution for collecting data of the same contextReduce redundant overheadReduce transported information to necessary minimumSDJS: include the physical layerUltra Fast and efficient: typ. 1000x faster Probabilistic, but adjustable accuracy/reliability (trade-off)

Albert Krohn, Michael Beigl, Sabin Wendhack, TecO, Universität Karlsruhe

SDJS – Activity Flow

Slotted (framed) Aloha Reduce Information to a

single jam signal Full distributed operation Hardware Requirements? Network Requirements? Collisions?

1. Station B starts SDJS2. Each node prepares its

transmission vector3. SDJS scheme is processed4. Each node has a reception

vector

Albert Krohn, Michael Beigl, Sabin Wendhack, TecO, Universität Karlsruhe

SDJS – The duck hunter problem

Estimation of the real number from a given number of signals (the reception vector)

Classical “Duck Hunter Problem” Solution: surjective mapping, partition theory

Group of hunters

How many hunterswere there?

Example:“How many devices are present in the cell?”

Albert Krohn, Michael Beigl, Sabin Wendhack, TecO, Universität Karlsruhe

SDJS – The Estimation 1

Duck hunter problem; analogon in SDJS:s Slotsk Devices sending one jam signal eacha received jam signals

=> P(a|k) Distribution

No a-priori information:Maximum Likelihood

kMLE=arg maxk P(a|k)

With a-priori information:Maximum a-posteriori

kMAP=arg maxk P(a|k) P(k)

Albert Krohn, Michael Beigl, Sabin Wendhack, TecO, Universität Karlsruhe

SDJS – The Estimation 2

How is estimation done in practice?

Start: count the number of received jam signals a

1. ML-Point estimation:Give an estimationFor k (MLE)

2. MAP-Confidence interval:Give an interval, [kmin,kmax] that contains the actual k with a given confidence (e.g. 90%)

In both cases: look-up table that can be prepared (no computation on nodes necessary)

Albert Krohn, Michael Beigl, Sabin Wendhack, TecO, Universität Karlsruhe

SDJS – Accuracy and Noise

Accuracy vs. Speed trade-off:accuracy depends on number of slots s

Noise:false positives and detection errors duringcarrier sense affect theestimation

Albert Krohn, Michael Beigl, Sabin Wendhack, TecO, Universität Karlsruhe

SDJS – The Implementation

TecO’s particle computer

Wireless sensor platform with 8Bit 20 Mhz processor

4kRAM, 4MBit Flash 125kbit/s wireless communication Customized ad hoc protocol

Find a partner <20ms Low power Low collisions

Development tools Over 1000 produced, large

developer community all over the world

Albert Krohn, Michael Beigl, Sabin Wendhack, TecO, Universität Karlsruhe

SDJS – The Experiment

Setting in an office with up to 50 particle computer

Impressive prove of concept:theory and real world setting are nearly identical

Albert Krohn, Michael Beigl, Sabin Wendhack, TecO, Universität Karlsruhe

SDJS – Conclusion

SDJS is An extension to wireless radio protocols Efficient group communication for very specific tasks Probabilistic by nature

SDJS can Efficiently and fast estimate parameters (1000x faster) Achieve adjustable accuracy (speed – accuracy trade off)

Overall performance of SDJS depends severely on the underlying technology

“SDJS: Efficient Statistics in Wireless Networks”

Albert Krohn, Michael Beigl, Sabin Wendhack

TecO (Telecooperation Office)Institut für TelematikUniversität Karlsruhe

www.teco.edu

Thank you for your attention!