1 Wireless Collisions: From Avoidance, to Recovery, to Creation Erran Li Aug. 2010.
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Transcript of 1 Wireless Collisions: From Avoidance, to Recovery, to Creation Erran Li Aug. 2010.
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
A4 A3 A2 A1Mapping π2
A2 A1 A4 A3Mapping π3
A3 A4 A1 A2Mapping π4
8
How permutation helps
Non-matching collisions on adjacent channels C1 and C2
Subcarrier 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 G2
Subtract A3
Decode B5 Subtract B5
B5
1212
Remap for matching collisions: Decoding graph
Decoding graph of collision at adjacent channels C1 and C2
A1A1
B3B3
A3A3
B5
Re-encode
Subtract
A4A4
B4B4
A2A2
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
A3
A4
S1 S2Sn
Time
Freq
Pa
B5
B2
B3
B4
A4 A3
A2
A1
S1 S2Sn
B2
B5
B4
B3
P′b
P′a
G1
G3
G2
G5
G4
G2
1
59
13
410
14
3
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
S2
R2
u1
u2
t=0
3535
GIAC Problem Formulation (cont’d)
Example: u1 has required channel state information
u1 can trigger S1 and S2 to transmit simultaneously
S1
R1
S2
R2
u1
u2
t=1
3636
GIAC Problem Formulation (cont’d)
Example: u1 has required channel state information
u1 can trigger S1 and S2 to transmit simultaneously
S1
R1
S2
R2
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
N
hBwwwwf
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
GIAC Algorithm for One-Hop Opportunities (cont’d)
1. Let PKT be the set of packets to be transmitted
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|
5. Let pkt be the one with minimal ni
6. PKT = PKT-{pkt}
7. done
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
Generalize the special case's optimal algorithm
4545
GIAC Algorithm for One-Hop Opportunities (cont’d)
Computing max non-interfering receivers of pkt i : 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
GIAC Algorithm for One-Hop Opportunities (cont’d)
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
GIAC Algorithm for One-Hop Opportunities (cont’d)
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
MatrixNet ArchitectureMatrixNet Architecture
Local Interference
Graph
Local Interference
Graph
Local Channel Information BaseLocal Channel Information Base
EstimatedLocal Node-pair
Channels
EstimatedLocal Node-pair
Channels
RoutingInformation
Base
RoutingInformation
Base
Routing/flow Information BaseRouting/flow Information Base
LocalFlowsLocalFlows
FairnessPolicy
FairnessPolicy
Management Information BaseManagement Information Base
Power Management
Policy
Power Management
Policy……
Forwarding QueueForwarding Queue
Overheard QueueOverheard Queue
MatrixNet Routing
MatrixNet MAC
Concurrency Selection
MatrixNetEncoding/Decoding
CoordinationVectors
MatrixNet Frame QueueMatrixNet Frame Queue
54
Estimated local node-pair Channels
(disseminate)
Estimated local node-pair Channels
(disseminate)
Local Interference
Graph
Local Interference
Graph
MatrixNet ArchitectureMatrixNet Architecture
Overheard packet cacheOverheard
packet cache
Concurrency Algorithm & Scheduler
Concurrency Algorithm & Scheduler
Inferred local flows
Inferred local flows
Pending packet queue
Pending packet queue
Encoding & decoding vectors
(disseminate)
Encoding & decoding vectors
(disseminate)
Coordinated transmissionCoordinated transmission
RoutingRouting
55
Retransmission ≠ Repeat: Simple Retransmission Permutation Can
Resolve Overlapping Channel Collisions
Li (Erran) LiBell 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 Networks
Li (Erran) LiBell Labs, Alcatel-Lucent
Joint work with: Richard Alimi (Yale), Dawei Shen (MIT), Harish Viswanathan (Bell Labs),
Richard Yang (Yale)