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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

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

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

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

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

Rate vs. Channel Gain:Bandwidth Optimized

  • TX coop needs large G to approach BC bound

  • MIMO bound unapproachable


General network geometry

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


Dpc vs relaying for different transmitter locations

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.


Capacity gain vs network topology

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 of tx and rx cooperation

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

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

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

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

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

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

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

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

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

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

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

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

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

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


Wireless network coding

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.


Generalized relaying

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 both interference and message

Beneficial to forward bothinterference and message


Achievable rates with simple network coding

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 a chieves capacity

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

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

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

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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