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SINR Diagram with Interference Cancellation. Merav Parter Joint work with Chen Avin , Asaf Cohen, Yoram Haddad, Erez Kantor, Zvi Lotker and David Peleg SODA 2012, Kyoto. Wireless Radio Networks. d. S 1. Stations with radio device Synchronous operation Wireless channel - PowerPoint PPT Presentation

PowerPoint Presentation

SINR Diagram withInterference Cancellation

Merav Parter

Joint work withChen Avin, Asaf Cohen, Yoram Haddad,Erez Kantor, Zvi Lotker and David Peleg

SODA 2012, Kyoto

11Stations with radio deviceSynchronous operationWireless channelNo centralized control

S1S2S3S4S5

Wireless Radio Networksd2Insert in clickReception Map - Who Hears Me?Vor(i) := Voronoi Cell of station siS.Each point ``hears the nearest stationVoronoi Diagram

M. Shamos and D. Hoey, FOCS '75 3Insert in click

Reception Map - Physical Model Point ``hears a station if it can decode its massageAttempting to model signal attenuation and interference explicitlySignal to Interference plus Noise Ratio (SINR)4Insert in clickPhysical Models: Signal to interference & noise ratio

Transmission EnergyPath-loss exponentReceived signal strength of station siReceiver pointStation siNoiseInterferenceStation si is heard at point p d - S iff

Fundamental Rule of the SINR modelReception Threshold (>1)66Increase font of SINRInterference Cancellation Receivers decode interfering signals

Cancel them from received message

Decode their intended messageThe optimal strategy in several scenarios(strong interference, spread spectrum communication, etc.)J.G. Andrews. Wireless Communications, IEEE, 20057Insert in clickSuccessive Interference Cancelation (SIC)

Received Signal

Interference

SignalDecode the Strongest

Interference

Received SignalDecode(Rounding) and subtract (cancel) it

Signal

Interference

Received SignalAmplify

10Can you hear me? (Uniform Powers)

s3s2s1s4Without SIC:pWith SIC:To ``hear s1, receiver p should cancel

signals of closer stations in order

11Can you hear me? (with IC)

s3s2s1s4p

NoNoNoYesYesYes

12The Power of SIC: Exponential Node Chain

Q: How many slots are required to schedule all links?

Without SIC: n slots are required for any power assignmentWith SIC: A single slot is required using uniform powersCan receive multiple messages at once!SINR Diagram

A map characterizing the reception zones of the network stationsReception Zone of Station si

Null ZoneCell := Maximal connected component within a zone.

CellAll stations transmit with power 1 (i=1 for every i)SINR Diagram with Uniform PowerTheorem:Every reception zone H(si) is convex and fat. H(si) Vor(i).

[Avin, Emek, Kantor, Lotker, Peleg, Roditty, PODC 2009]

[Avin et al. PODC09]

1515Reception Map for Physical Model with Interference Cancellation

Can I receive s1??How hears me?Goal: Uniform Power with SIC16SIC-SINR DiagramNo Cancellation1- Cancellation2- CancellationA map characterizing the reception zone of stations in the SINR where receivers employ ICReception Map for Station s1

Complexity of SIC-SINR DiagramThe polynomial depends on cancellation ordering.Aprioi there are exponentially many.SIC-SINR reception zones are not convex in d nor hyperbolically convex in d+1.

1818The Map Drawing ChallengeAre there exponentially many cells?

How to draw the reception zone of a given station under IC setting?What is the characteristic polynomial of the zone?Depends on cancellation ordering,but a priori there are exponentially many19ChallengesNice Properties of ZonesBounding#Cells (how many?)Map Drawing (which are they?)Point LocationTask(how to store them?)AlgorithmsTopology

2020Reception Region of Cancellation Ordering

H(s1)H(s2, s1)H(s2, s3, s1)H(s3, s2, s1)H(s3, s1)

Reception Region of Cancellation Ordering (CO)

H(s2)H(s1|S-{s2})High-Order Voronoi DiagramExtension of the ordinary Voronoi diagram

Cells are generated by more than one point in S.

Every region consists of locations having the same closest points in S.

Order k=2Cells generatorsM. Shamos and D. Hoey, FOCS '75 23'order' means that number of points constituting a generator and 'higher' means more than one point. Note that 'higher' does not refer to the dimension of a space.

Ordered order-k Voronoi Diagram

Or, inductivelySorted list of generatorsFor k=2

24a singularity is in general a point at which a given mathematical object is not definedHigh-Order Voronoi Diagram and SIC-SINR Diagram

25a singularity is in general a point at which a given mathematical object is not definedThe Topology of Reception Zone with SICThe Reception zone of every networks station is a collection of O(n2d) shapes.

Each shape is:

Convex

Correspond to distinct cancellation ordering

Fully contained in the high-order Voronoi cell

26a singularity is in general a point at which a given mathematical object is not definedDrawing Map: Introducing Hyperplane Arrangement

Labelled Arrangement(1,2,3)(1, 3,2)Stations ordering is required only onceObserve:

(3, 1, 2)(3 , 2, 1)(2, 3 , 1)(2, 1, 3 )p28a singularity is in general a point at which a given mathematical object is not definedDrawing SIC-SINR Reception MapFor station s1(1,2,3)(1, 3,2)( 3,1,2)( 3,2,1)( 2,3,1)( 2,1,3)112,13,13,2,12,3,1

29a singularity is in general a point at which a given mathematical object is not definedBounding #Cells The Compactness Parameter Reception Threshold (>1)Path-loss exponent30a singularity is in general a point at which a given mathematical object is not definedBounding #Cells31a singularity is in general a point at which a given mathematical object is not definedChallengesNice Properties of ZonesBounding#Cells (how many?)Map Drawing (which are they?)Point LocationTask(how to store them?)AlgorithmsTopology

3232Challenges What We Know#Cells General- O(n2d)Compact network- O(1)Map DrawingEfficient constructionof labeled arrangement O(n2d+1)Point Location TaskPoly-time construction.Logarithmic time per queryAlgorithmsTopology

Nice Properties of ZonesCollection of convex cellsEach related to high-orderVoronoi cell.

3333Questions?

Thanks for listening!3434