A General Algorithm for Interference Alignment and Cancellation in Wireless Networks

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A General Algorithm for Interference Alignment
and Cancellation in Wireless Networks

• Li (Erran) Li
• Bell Labs, Alcatel-Lucent
• Joint work with Richard Alimi (Yale), Dawei Shen
  (MIT), Harish Viswanathan (Bell Labs), Richard
  Yang (Yale)

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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

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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

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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 a in 2,3) and random placement
  Ozgur, Leveque and Tse, IEEE Trans. Info.
  Theory07
• Optimal scaling requires cooperative transmission
  when node placements are less regular Niesen,
  Gupta and Shah08

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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

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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 ?
• Assume channel matrix H is known
• Y HXN X input, Y output, N noise

Ri
hij
Sj
A snapshot of a local neighborhood
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GIAC Problem Formulation (contd)

• How to enable simultaneous transmissions?

Receiver interference cancellation
Sender pre-coding
Goal
where is a diagonal matrix Thus,
yi?ixiNi
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GIAC Problem Formulation (contd)

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

S1
u1
R1
R2
S2
u2
t0
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GIAC Problem Formulation (contd)

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

S1
u1
R1
R2
S2
u2
t1
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GIAC Problem Formulation (contd)

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

S1
u1
R1
R2
S2
u2
t2
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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

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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

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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
Ri
Sj
Rj
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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 PKTgtminni pkti PKT
4. Let pkt be the one with minimal ni
5. PKT PKT-pkt
6. done

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GIAC Optimal Algorithm for a Special Case
(contd)

• Example

S4
S1
R1
pkt1, pkt2
n3ltpkt1, pkt2 , pkt3
S2
pkt1 , pkt2 minn1 , n2
R2
Stop!
S3
R3
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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
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GIAC Algorithm for One-Hop Opportunities (contd)

• Convex programming to compute feasibility

Notation H channel matrix m number of
senders k number of receivers ? coding
coefficient matrix P max power Ni noise at
receiver Ri
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GIAC Algorithm for One-Hop Opportunities (contd)

• Let PKT be the set of packets to be transmitted
• Create pseudo senders for any packet pkt a
  receiver has
• While NotFeasible(PKT, H, ?)
• ni maxNonIntR(PKT, H, i), i1,2,,PKT
• Let pkt be the one with minimal ni
• PKT PKT-pkt
• 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 PKTgt minni pkti PKT
4. Let pkt be the one with minimal ni
5. PKT PKT-pkt
6. done

Generalize the special case's optimal algorithm
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GIAC Algorithm for One-Hop Opportunities (contd)

• 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

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GIAC Algorithm for One-Hop Opportunities (contd)

• Example

R1
M12
S1
S2
Receivers not interfered by pkt1 R3
L11
R2
S3
n1 M1 L13
R3
Similarly, n2 M2 L2123
n3 M3 L3213
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GIAC Algorithm for One-Hop Opportunities (contd)

• Example 2

S1
R1
Create pseudo senders
S2
R2
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GIAC Implementation in GNU Radio

• Time synchronization
• Only need to synchronize within cyclic prefix
• Sampling rate 500KHz

Drift within 0.75 samples/sec
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GIAC Implementation in GNU Radio (contd)

• Channel estimation and feedback
• Need amplitude and phase offset
• Stable phase offset estimate difficult in GNU
  radio
• Current estimation error 1520Hz
• Feedback delay software processing delay,
  hardware--software latency

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Related Work

• Practical interference cancellation techniques
• Networked MIMO Samardzija et al, Bell Labs
  Project 2005now
• Physical/analog layer network coding Zhang et
  al, MOBICOM06, Katti et al, SIGCOMM07
• Interference alignment and cancellation
  Gollakota, Perli, Katabi, SIGCOMM09

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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?

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Q and A
Thank you
Questions?
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MatrixNet Architecture
MatrixNet Architecture
MatrixNetEncoding/Decoding
MatrixNet Routing
MatrixNet MAC
Concurrency Selection
CoordinationVectors
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Routing
Local Interference Graph
Encoding decoding vectors (disseminate)
Concurrency Algorithm Scheduler
Estimated local node-pair Channels (disseminate)
Coordinated transmission
Overheard packet cache
Pending packet queue
Inferred local flows
MatrixNet Architecture