EE360: Lecture 9 Outline

AnnouncementsMakeup lecture this Friday, 2/7, 12-1:15pm

in Packard 312Revised proposal due Monday 2/10HW 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

TX2

RX1

RX2

4

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,”

5

Rate vs. Channel Gain:

Bandwidth Optimized

TX coop needs large G to approach BC bound MIMO bound unapproachable

6

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).

RX1

RX2

y1

y2

TX1x1

TX2x2

x1TX1

d=1

d=r<1

7

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

Capacity Gainvs Network Topology

Cooperative DPC best

Cooperative DPC worst

RX2

y2

TX1x1

x2

x1

d=1

d=r<1

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,”

10

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 cooperationBest known achievable rate when Rx and

relay close

Capacity Evaluation

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-opRx 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

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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

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Best cooperation strategy

Cooperation performance depends on CSI, topology, and power adaptation.TX co-op is best with full CSI and

power adaptationRX co-op best with power

optimization and receiver phase CSINo 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-orthogonalCF rate

Non-orthogonal DF rate

Non-orthogonal Cut-set bound

Iterative conferencingvia 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 lossApplicable for clusters, since

cooperation band can be reused spatially.

DF vs. CFDF: nearly optimal when transmitter and

relay are closeCF: 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 SNRHigh 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 linksOther 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

source 1

source 2

relay

destination 2

destination 1

message W1

Relay switches between forwarding two data streams

message W2

W2

W1

This setting still implies routing on the network layer

Network Coding

source 1

source 2

relay

destination 2

destination 1

Combining data streams on the relay is crucialAssumptions: non-wireless setting

no interference no broadcastingLandmark paper by Ashlwede et. al.: achieves multicast capacity

a

b

a+b

a+b

Wireless Network Coding

Alternative to store and forward Can forward message and/or

interference Large capacity gains possible Many practical issues

TX1

TX2

relay

RX2

RX1X1

X2

Y3=X1+X2+Z3

Y4=X1+X2+X3+Z4

Y5=X1+X2+X3+Z5

X3= f(Y3)

“XORs in the Air: Practical Wireless Network Coding”, Katti et. al.

Generalized Relaying

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

TX1

TX2

relay

RX2

RX1X1

X2

Y3=X1+X2+Z3

Y4=X1+X2+X3+Z4

Y5=X1+X2+X3+Z5

X3= f(Y3) Analog network coding

Beneficial to forward bothinterference and message

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Achievable Rates with Simple Network

Coding

Transmitted at the relay:

Received at destination t:

X3=αY3

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

Achievable rate region for the considered channel

Assumption: No delay

53215

43214

)1()1(

)1()1(

ZZXXY

ZZXXY

Compound MAC

S DPs

P1

P2

P3

P4

Simple scheme achieves capacity

S DPs

P1

P2

P3

P4

• For large powers Ps, P1, P2, analog network coding approaches capacityGerard’s talk will discuss practical wireless network coding

Generalizes to Large Network

network of relayssourcesdestinations

… …

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

1

M

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 decadesPrimarily good in multicast settingsIt’s application to wireless still relatively

untapped

Today’s presentation

Gerard will 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