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EE360: Lecture 9 Outline. Announcements Makeup lecture this Friday, 2/7, 12-1:15pm in Packard 312 Revised proposal due Monday 2/10 HW 1 posted, due 2/19 Cooperation in Ad Hoc Networks V irtual MIMO TX and RX Cooperation Conferencing Network coding. Cooperation in Wireless Networks.

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EE360: Lecture 9 Outline

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EE360: Lecture 9 Outline

  • Announcements

    • Makeup lecture this Friday, 2/7, 12-1:15pm in Packard 312

    • Revised proposal due Monday 2/10

    • HW 1 posted, due 2/19

  • Cooperation in Ad Hoc Networks

  • Virtual MIMO

  • TX and RX Cooperation

  • Conferencing

  • Network coding


Cooperation in Wireless Networks

  • Routing is a simple form of cooperation

  • Many more complex ways to cooperate:

    • Virtual MIMO , generalized relaying, interference forwarding, and one-shot/iterative conferencing

  • Many theoretical and practice issues:

    • Overhead, forming groups, dynamics, synch, …


Virtual MIMO

  • TX1 sends to RX1, TX2 sends to RX2

  • TX1 and TX2 cooperation leads to a MIMO BC

  • RX1 and RX2 cooperation leads to a MIMO MAC

  • TX and RX cooperation leads to a MIMO channel

  • Power and bandwidth spent for cooperation

TX1

RX1

RX2

TX2


Rate vs. Channel Gain*Cooperation Bandwidth “Free”

  • Symmetric Case: Cooperative channel gain G

  • As G increases, approach upper bounds

C. Ng, N.Jindal, A.. Goldsmith, and U. Mitra,

“Capacity Gain from Two-Transmitter and Two-Receiver Cooperation,”


Rate vs. Channel Gain:Bandwidth Optimized

  • TX coop needs large G to approach BC bound

  • MIMO bound unapproachable


d=r<1

x1

TX1

x1

TX1

d=1

General Network Geometry

  • For TX1 and TX2 close together, exchanging messages to do DPC doesn’t cost much.

  • As TX1 approaches receivers, cooperation cost increases.

    • Might be better to use TX1 as a relay for TX2, or a combination of broadcasting and relaying.

    • Optimal strategy will depend on relative distances.

  • What are the tradeoffs for the different cooperation strategies.

    • No receiver cooperation (RXs close, little cooperation gain).

y1

RX1

RX2

y2

TX2

x2


Cooperative DPC best

Cooperative

DPC worst

DPC vs. Relaying for different Transmitter Locations

  • Transmitters close:

    • Cooperative DPC has highest sum rate.

  • Transmitters far:

    • Much power needed for cooperative DPC

    • Intermediate node more useful as relay.


Cooperative DPC best

Cooperative

DPC worst

d=r<1

x1

x1

TX1

y2

x2

d=1

Capacity Gainvs Network Topology

RX2

Optimal cooperation coupled with access and routing


Relative Benefits ofTX and RX Cooperation

  • Two possible CSI models:

    • Each node has full CSI (synchronization between Tx and relay).

    • Receiver phase CSI only (no TX-relay synchronization).

  • Two possible power allocation models:

    • Optimal power allocation: Tx has power constraint aP, and relay (1-a)P ; 0≤a≤1 needs to be optimized.

    • Equal power allocation (a = ½).

Chris T. K. Ng and Andrea J. Goldsmith,

“The Impact of CSI and Power Allocation on Relay Channel Capacity and Cooperation Strategies,”


Capacity Evaluation

  • Cut-set upper bound for TX or RX cooperation

  • Decode-and-forward approach for TX cooperation

    • Best known achievable rate when RX and relay close

  • Compress and forward approach for RX cooperation

    • Best known achievable rate when Rx and relay close


Example 1: Optimal power allocation with full CSI

  • Cut-set bounds are equal.

  • Tx co-op rate is close to the bounds.

  • Transmitter cooperation is preferable.

Tx & Rx cut-set bounds

Tx co-op

Rx co-op

No co-op


Example 2: Equal power allocation with RX phase CSI

  • Non-cooperative capacity meets the cut-set bounds of Tx and Rx co-op.

  • Cooperation offers no capacity gain.

Non-coop capacity

Tx & Rx cut-set bounds


Example 3: Equal power allocation with RX phase CSI

  • Non-cooperative capacity meets the cut-set bounds of Tx and Rx co-op.

  • Cooperation offers no capacity gain.

Non-coop capacity

Tx & Rx cut-set bounds


Best cooperation strategy

  • Cooperation performance depends on CSI, topology, and power adaptation.

    • TX co-op is best with full CSI and power adaptation

    • RX co-op best with power optimization and receiver phase CSI

    • No capacity gains from cooperation under fixed power and receiver phase CSI

  • In TX cooperation power allocation is not essential, but full CSI (synchronous-carrier) is necessary.

  • In RX cooperation only RX CSI (asynchronous-carrier) is utilized, but optimal power allocation is required.

  • Similar observations hold in Rayleigh fading.


Capacity: Non-orthogonal Relay Channel

  • Compare rates to a full-duplex relay channel.

  • Realize conference links via time-division.

  • Orthogonal scheme suffers a considerable performance loss, which is aggravated as SNR increases.

Non-orthogonal

Cut-set bound

Non-orthogonal

DF rate

Non-orthogonal

CF rate

Iterative conferencing

via time-division


Transmitter vs. Receiver Cooperation

  • Capacity gain only realized with the right cooperation strategy

  • With full CSI, Tx co-op is superior.

  • With optimal power allocation and receiver phase CSI, Rx co-op is superior.

  • With equal power allocation and Rx phase CSI, cooperation offers no capacity gain.

  • Similar observations in Rayleigh fading channels.


Conferencing Relay Channel

  • Willems introduced conferencing for MAC (1983)

    • Transmitters conference before sending message

  • We consider a relay channel with conferencing between the relay and destination

  • The conferencing link has total capacity C which can be allocated between the two directions

“Iterative and One-shot Conferencing in Relay Channels”, Ng. Maric, Goldsmith


Iterative vs. One-shot Conferencing

  • Weak relay channel: the iterative scheme is disadvantageous.

  • Strong relay channel: iterative outperforms one-shot conferencing for large C.

One-shot: DF vs. CF

Iterative vs. One-shot


Lessons Learned

  • Orthogonalization has considerable capacity loss

    • Applicable for clusters, since cooperation band can be reused spatially.

  • DF vs. CF

    • DF: nearly optimal when transmitter and relay are close

    • CF: nearly optimal when transmitter and relay far

    • CF: not sensitive to compression scheme, but poor spectral efficiency as transmitter and relay do not joint-encode.

  • The role of SNR

    • High SNR: rate requirement on cooperation messages increases.

    • MIMO-gain region: cooperative system performs as well as MIMO system with isotropic inputs.


Cooperation in Routing:Generalized Relaying

  • Traditional communication in a wireless network: multihop through logical point-to-point links

    • Other signals considered to be interference

  • Cooperative strategies developed for the relay channel

    • Nodes do not discard interfering signals

    • Cooperatively encode

“Generalized Relaying in the Presence of Interference,” Maric, Dabora, Goldsmith,


Routing on the Network Layer

messageW1

  • Relay switches between forwarding two data streams

W2

destination 1

source 1

relay

messageW2

W1

source 2

destination 2

This setting still implies routing on the network layer


Network Coding

destination 1

source 1

a

a+b

relay

a+b

b

source 2

destination 2

  • Combining data streams on the relay is crucial

  • Assumptions: non-wireless setting

    • no interference

    • no broadcasting

    • Landmark paper by Ashlwede et. al.: achieves multicast capacity


RX1

TX1

X1

Y4=X1+X2+X3+Z4

relay

Y3=X1+X2+Z3

X3= f(Y3)

Y5=X1+X2+X3+Z5

X2

TX2

RX2

WirelessNetwork Coding

  • Alternative to store and forward

  • Can forward message and/or interference

  • Large capacity gains possible

  • Many practical issues

“XORs in the Air: Practical Wireless Network Coding”,

Katti et. al.


RX1

TX1

X1

Y4=X1+X2+X3+Z4

relay

Y3=X1+X2+Z3

X3= f(Y3)

Y5=X1+X2+X3+Z5

X2

TX2

RX2

Generalized Relaying

Analog network coding

  • Can forward message and/or interference

    • Relay can forward all or part of the messages

      • Much room for innovation

    • Relay can forward interference

      • To help subtract it out


Beneficial to forward bothinterference and message


Compound MAC

Achievable Rates with Simple Network Coding

P3

P1

Transmitted at the relay:

Received at destination t:

X3=αY3

Ps

D

S

P2

P4

  • Capacity region of Compound MAC is known [Ahslwede,1974]

    Achievable rate region for the considered channel

    • Assumption: No delay


Simple scheme achieves capacity

P3

P1

Ps

D

S

P2

P4

  • For large powers Ps, P1, P2, analog network coding approaches capacity

Gerard’s talk will discuss practical wireless network coding


Generalizes to Large Network

sources

network of relays

destinations

1

M

  • Achievable rates of the same network coding scheme can be evaluated in a large network with M>2 destinations


Summary

  • Many techniques for cooperation in ad hoc networks

  • Virtual MIMO can provide gain when TX nodes close and RX nodes close, otherwise relaying better

  • Conferencing allows for iterative decoding, similar to LDPC decoding – can be very powerful

  • Network coding is the biggest innovation in routing in several decades

    • Primarily good in multicast settings

    • It’s application to wireless still relatively untapped


Today’s presentation

Gerardwill present “XORs in the Air: Practical Wireless Network Coding”

Authors: S. Katti, H. Rahul, W. Hu, D. Katabi, M. Medard, J.Crowcroft

Published in: IEEE/ACM Transactions on Networking, June 2008


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