Wireless Collisions: From Avoidance, to Recovery, to Creation

1

Wireless Collisions: From Avoidance, to Recovery, to Creation

Erran Li

Aug. 2010

22

Talk Outline

Recovery: remap Collision “creation”: interference alignment

3

Wireless networks with overlapping channels

Chaotically deployed WiFi networks Each user chooses its own channel

Planned WiFi networks Due to shortage of orthogonal channels, partially

overlapped channels are beneficial [Misra et al, SIGMETRICS’06]

WiFi networks built on digital white space, e.g. WhiteFi [Bahl et al. SIGCOMM’09]

4

802.11g overlapping channel collision problem

Bob

APa on channel Ca

Collision!

Alice

APb on channel Cb

Collision!

Chuck

5

802.11g overlapping channel collision problem

Bob

APa on channel Ca

More Collision!

Alice

APb on channel Cb

More Collision!

Chuck

Retransmission

66

802.11 background

Using 802.11g as an example Each channel has 4 groups of

subcarriers: C1 consists of G1, G2, G3, G4; C2 consists of G2, G3, G4, G5

C1 and C2 are overlapping adjacent channels;

C1 and C3 are overlapping non-adjacent channels

Bits are assigned to subcarriers E.g. bit sequences Ai is assigned

to subcarrier Gi, i=1,2,3,4

Subcarrier Group

G1 G2 G3 G4

A1 A2 A3 A4

77

Remap basic idea: structured permutation

Subcarrier Group

G1 G2 G3 G4

A1 A2 A3 A4Mapping π1




8

How permutation helps Non-matching collisions on adjacent channels C1

and C2Subcarrier Group

G1 G2 G3 G4

A1 A2 A3 A41st transmission

2nd transmission A4 A3 A2 A1

A2 A1 A4 A33rd transmission

A3 A4 A1 A24th transmission

99

How permutation helps (cont’d) Non-matching collisions on non-adjacent channels

C1 and C3

Subcarrier Group

G1 G2 G3 G4

A1 A2 A3 A41st transmission

2nd transmission A4 A3 A2 A1

10

Remap basic idea: Matching-collision setting

Collision!

Alice Bob

Collision!

APa on channel Ca

APb on channel Cb

Matching collisions on adjacent channels

11

Remap for matching collisions Matching collisions on adjacent channels C1 and C2

A1 A2 A3 A4

B5B2 B3 B4

Subcarrier Group

G1 G2 G3 G4

G5A4 A3 A2 A1

B2B5 B4 B3

G1 G2 G3 G4

G5

Decode A1 Re-encode A1 on G4

Decoded bits:

Subtract A1Subtract A1

A1

Decode B3 Re-encode B3 on G3

Subtract B3 Subtract B3

B3

Decode A3

A3

Subtract A3 Re-encode A3 on G2Subtract A3

Decode B5 Subtract B5

B5

1212

Remap for matching collisions: Decoding graph

Decoding graph of collision at adjacent channels C1 and C2

A1 A1

B3B3

A3 A3

B5

Re-encode

Subtract

A4 A4

B4B4

A2 A2

B2

1st collision 2nd Collision 1st collision 2nd Collision

13

Remap for matching collisions: a time-frequency view

collisions at adjacent channels C1 and C2 : a time and frequency view

Pb

∆1∆2

A1 A2

A3A4

S1 S2Sn

Time

Freq

Pa

B5

B2

B3B4

A4 A3

A2A1

S1 S2Sn

B2

B5

B4B3

P′b

P′a

G1

G3

G2

G5

G4G2

1

59

13

410

143

711

2

68

12

14

Remap for matching collisions

Theorem on a pair of matching collisions: Assume that Alice and Bob use different permutations for

the two transmissions, Alice’s AP and Bob’s AP can each decode both packets despite collisions.

1515

Remap Details

Encode bit-to-subcarrier mapping Design 4 long PN sequence long training symbols

Detecting collision Cross-correlate 4 long training symbol pairs

Detecting matching collision Correlating subcarrier group Gi and its remapped

subcarriers Detecting modulation

Cannot decode PLCP header of Bob’s packet Solution: raw sample subtraction for the first pass

16

Remap Details (cont’d) Loss of orthogonality

Carrier frequency offset Desired symbol and

interfering symbol unalignment

Desired signal at subcarrier i:

Interfering signal at subcarrier i+m:

Aligned interference symbols on non-adjacent subcarriers have zero Interference energy.

17

Remap Details (cont’d) Loss of orthogonality

Carrier frequency offset Desired symbol and

interfering symbol unalignment

Desired signal at subcarrier i:

Interfering signal at subcarrier i+m: Interference energy:

The energy is 19dB lower if m=4;

21dB lower if m=5

1818

Remap Details (cont’d)

802.11 channel specifics: dealing with used subcarrier groups

1919

Evaluation

Experimental setup for non-matching collisions: Use MSRA Sora software-radio platform for 802.11g Fix Alice at channel 3 For adjacent-channel collision test, Bob (the interferer) is

at channel 4; for non-adjacent channel collision test, Bob is at channel 5

2020

Evaluation (cont’d)

Performance metric Normalized throughput: actual number of decoded

packets divided by the ideal number of decoded packets

2121

Evaluation: collision detection

Collision detection under different SINR settings

2222

Evaluation: collision matching

False positive: if matching wrong pairs False negative: if fails to match a collision pair

2323

Evaluation: non-adjacent channel

BER and throughput ratio under different SNR settings

2424

Evaluation: Adjacent Channel

BER vs SNR difference between channel 3 and 4

2525

Throughput ratio vs SNR difference between channel 3 and 4

Evaluation: adjacent channel (cont’d)

2626

Remap: Future Work

Generalize Remap to other channel structures Investigate techniques that deal with loss-of-

orthogonality issue Evaluate how well matching collision detection and

decoding work Extend Remap to dynamic spectrum access

networks

2727

Talk Outline

Recovery: remap

-> Collision “creation”: interference alignment

2828

Talk Outline

Wireless mesh network design General interference alignment and cancellation (GIAC)

problem Design overview Problem formulation Computational complexity Algorithm

GNU radio testbed implementation Related work Conclusion and future work

2929

Limitation of Conventional Mesh Network Design

Current mesh networks have limited capacity [dailywireless.org]

Increased popularity of video streaming and large downloads will only worsen congestion

Network-wide transport capacity does not scale [Gupta and Kumar 2001]

O( ) where n is the number of users Traditional design limitations:

Treats wireless transmission as a point-to-point link for unicast

Treats interference from other transmissions as noise

n

3030

A New Paradigm for Mesh Network Design

Wireless networks propagate information rather than transporting packets Physical layer: interference cancellation, zero forcing,

interference alignment Network coding

Capacity scales better in this new paradigm for α in [2,3) and random placement [Ozgur, Leveque

and Tse, IEEE Trans. Info. Theory’07]

Optimal scaling requires cooperative transmission when node placements are “less regular” [Niesen, Gupta and Shah’08]

2n

3131

GIAC Design Overview

Goal: increase concurrency through interference cancellation techniques

Design constraints and guidelines

Global cooperation not practical: cooperate locally

No explicit exchange of data packets for cooperation: exploit naturally occurring opportunities

Channel state information essential for any cooperative techniques: exchange only channel state information and necessary signaling messages

3232

GIAC Problem Formulation

Objective: find the max number of simultaneous transmissions

Connectivity graph G=(V, E) Interference graph GI=(V, EI) A set of senders S V A set of receivers R V Receiver can be one or two hops away

from sender pkti is destined to Ri Each node u has a packet pool Lu which

records overheard packets Assume transmission rate is fixed at ρ Assume channel matrix H is known

Y = HX+N; X: input, Y: output, N: noise

A snapshot of a local neighborhood

Sj

Ri

hij

3333

GIAC Problem Formulation (cont’d) How to enable simultaneous transmissions?

NXΦXΦHY 21 Goal: where is a diagonal matrix

Thus, yi=λixi+Ni

Sender pre-coding

Receiver interference cancellation

ΦH 2

3434

GIAC Problem Formulation (cont’d)

Example: u1 has required channel state information u1 can trigger S1 and S2 to transmit simultaneously

S1

R1

S2R2

u1

u2

t=0

3535



S1

R1

S2R2

u1

u2

t=1

3636



S1

R1

S2R2

u1

u2

t=2

3737

Talk Outline

Wireless mesh network design General interference alignment and cancellation (GIAC)

problem Design overview Problem formulation Computational complexity Algorithm

GNU radio testbed implementation Related work Conclusion and future work

3838

GIAC Complexity: Sender Side

Computational complexity matters because algorithm runs in fast path

The interference control problem is NP-hard Consider a special case where the packet pool at each

node is empty Reduction from max independent set

for each e=(vi, vj), create a gadget with sender Si, Sj, and receiver Ri, Rj where Si, Sj has pkti, pktj

Si

Sj

Ri

Rj

3939

GIAC Complexity: Receiver Side

The problem is NP-hard Reduction from clique: given G=(V,E), for each e=(vi,

vj), create a gadget with sender Si, Sj, and receiver Ri, Rj where Si, Sj has pkti, pktj and receiver Ri, Rj has pktj, pkti

Assume H has full rank (no channel alignments)Si

Sj

Ri

Rj

4040

GIAC: Optimal Algorithm for a Special Case

Assumptions No receiver-side cancellation Channel matrix H has full rank (ignore channel alignment cases) No power constraint

Key intuition: for each transmitted packet pkti, need an independent packet pkti to cancel its interference at each receiver

1. Let PKT be the set of packets to be transmitted

2. For each pkti, Let ni be the number of senders

3. While |PKT|>min{ni | pkti PKT}

4. Let pkt be the one with minimal ni

5. PKT = PKT-{pkt}

6. done

4141

GIAC: Optimal Algorithm for a Special Case (cont’d)

S1

S2

S4

R1

R2

S3 R3

pkt1,pkt2, pkt3:

n1, n2, n3: 2 2 1

Example

{pkt1, pkt2}

|{pkt1 , pkt2}| = min{n1 , n2} Stop!

n3<|{pkt1, pkt2 , pkt3}|

4242

GIAC Algorithm for One-Hop Opportunities

Feasibility problem: Given a set of packets and

power constraint at each sender, can they be transmitted at the same time at a given rate?

Yes, a feasible solution does not exist iff there exists W s.t. R)(WMax],,[W

R

[ρ, …, ρ]

W

R

4343

GIAC Algorithm for One-Hop Opportunities (cont’d)

Convex programming to compute feasibility

0

1

..

)],,,[( minimize

1

121

i

K

ii

K

iik

w

w

ts

wwwwf

k

jij

ij

k

i i

iiik

Pmi

hkjiji

HHts

NhBwwwwf

1

2

'

'

1

2'

221

|| :1

0 : ,1 ,

..

)||1(logmax)],,,[(

Notation:H: channel matrixm: number of sendersk: number of receiversФ: coding coefficient matrixP: max powerNi: noise at receiver Ri

4444



2. Create pseudo senders for any packet pkt a receiver has

3. While NotFeasible(PKT, H, ρ)

4. ni = maxNonIntR(PKT, H, i), i=1,2,…,|PKT|


6. PKT = PKT-{pkt}

7. done


2. For each pkti, Let ni be the number of senders

3. While |PKT|> min{ni | pkti PKT}


5. PKT = PKT-{pkt}

6. done

Generalize the special case's optimal algorithm

4545


Computing max non-interfering receivers of pkti : maxNonIntR(PKT, H, i) Find the maximum matching Mi between senders with pkti

and receivers in interference graph; Let Li be the set of receivers not interfered by pkti and not

in the matching maxNonIntR(PKT, H, i) = | Mi | + | Li |

4646


Example

S1

R1

S2

S3

R2

R3

Receivers not interfered by pkt1: {R3}

Similarly, n2= |M2|+ |L2|=1+2=3; n3= |M3|+ |L3|=2+1=3

|M1|=2

|L1|=1

n1 = |M1|+ |L1|=3

S1 R1

S2 R2

Max matching of pkt1

4747


Example 2

S1R1

S2 R2

Create pseudo senders

R1

R2

S1

S2

S3

S4

4848

GIAC Implementation in GNU Radio

Time synchronization Only need to synchronize within

cyclic prefix Sampling rate 500KHz

Drift within 0.75 samples/sec

Drift within 0.75 samples/sec

49

GIAC Implementation in GNU Radio: (cont’d)

Channel estimation and feedback Need amplitude and phase offset Stable phase offset estimate difficult in GNU radio

Current estimation error: 15~20Hz Feedback delay: software processing delay, hardware--

software latency

5050

Related Work

Practical interference cancellation techniques Networked MIMO [Samardzija et al, Bell Labs Project 2005~now] Physical/analog layer network coding [Zhang et al, MOBICOM’06,

Katti et al, SIGCOMM’07]

Interference alignment and cancellation [Gollakota, Perli, Katabi, SIGCOMM’09]

5151

Conclusion and Future Work

We have designed algorithms and protocols for opportunistic interference control

Ongoing and future work Implementation related

Channel phase shift estimation and feedback Other implementation platforms, e.g. Bell Labs networked MIMO

platform or MSR Sora? How to solve the problem when there are multiple

antennas? Information theory related

How much does dirty paper coding help? Can our interference control scheme achieve optimal capacity

scaling in networks with “less regular” node deployments?

5252

Q and A

Questions?

53

MatrixNet Architecture


Local Interference

Graph

Local Channel Information Base

EstimatedLocal Node-pair

Channels

RoutingInformation

Base

Routing/flow Information Base

LocalFlows

FairnessPolicy

Management Information BasePower

ManagementPolicy

…

Forwarding Queue

Overheard Queue

MatrixNet Routing

MatrixNet MAC

Concurrency Selection

MatrixNetEncoding/Decoding

CoordinationVectors

MatrixNet Frame Queue

54

Estimated local node-pair Channels

(disseminate)

Local Interference

Graph


Overheard packet cache

Concurrency Algorithm & Scheduler

Inferred local flows

Pending packet queue

Encoding & decoding vectors

(disseminate)

Coordinated transmission

Routing

55

Retransmission ≠ Repeat: Simple Retransmission Permutation Can

Resolve Overlapping Channel CollisionsLi (Erran) Li

Bell Labs, Alcatel-Lucent

Joint work with: Kun Tan(MSR, Beijing), Ying Xu(Beijing University of Post and

Telecommunication), Harish Viswanathan (Bell Labs), Yang Richard Yang (Yale)

56

A General Algorithm for Interference Alignment and

Cancellation in Wireless NetworksLi (Erran) Li

Bell Labs, Alcatel-Lucent

Joint work with: Richard Alimi (Yale), Dawei Shen (MIT), Harish Viswanathan (Bell Labs),

Richard Yang (Yale)

Documents

Wireless Collisions: From Avoidance, to Recovery, to Creation