A General Algorithm for Interference Alignment and Cancellation in Wireless Networks

1

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)

22

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

33

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

44

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

55

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

66

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

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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

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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

99



S1

R1

S2R2

u1

u2

t=1

1010



S1

R1

S2R2

u1

u2

t=2

1111

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

1212

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

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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

Sj

Ri

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 |PKT|>min{ni | 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 (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}|

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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)(WMax],,[W

R

[ρ, …, ρ]

W

R

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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

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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

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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 |

2020


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

2121


Example 2

S1R1

S2 R2

Create pseudo senders

R1

R2

S1

S2

S3

S4

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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

Drift within 0.75 samples/sec

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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

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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]

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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

Questions?

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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

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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

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A General Algorithm for Interference Alignment and Cancellation in Wireless Networks