1. EE360: Lecture 9 Outline Announcements Cooperation in Ad Hoc Networks
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

2. 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, …

3. 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 and TX2 are close to each other, RX1 and RX2 are close to each other – therefore natural for them to cooperate
Stress that TX’s have independent messages to send to RX’s
All in terms of CAPACITY

4. Rate vs. Channel Gain* Cooperation Bandwidth “Free”
C. Ng, N.Jindal, A.. Goldsmith, and U. Mitra,
“Capacity Gain from Two-Transmitter and Two-Receiver Cooperation,”
Symmetric Case: Cooperative channel gain G
As G increases, approach upper bounds

5. Rate vs. Channel Gain: Bandwidth Optimized
TX coop needs large G to approach BC bound
MIMO bound unapproachable

6. General Network Geometry
d=1
d=r<1
TX1 x1 x1
TX1 y1
RX1 y2
RX2
TX2 x2
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).
Strong interference means gain of interference same as signal gain (1 in this case)
- for this interference channel, both receivers decode both messages
- capacity region upper bounded by each receivers MAC, and this bound is tight.
- due to sum power constraint P, capacity region bounded by R1+R2<=log(1+P)
- This set of rates also achiveable via TDMA, plot sum rate point on graphs
TX1 and TX2 are close to each other, RX1 and RX2 are close to each other – therefore natural for them to cooperate
Stress that TX’s have independent messages to send to RX’s
All in terms of CAPACITY

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

8. Capacity Gain vs Network Topology
TX1 x1 x2
d=1
d=r<1
Cooperative DPC best
Cooperative
DPC worst
in a fading environment in the absence of CSIT, equal
power allocation is optimal and capacity-achieving at high SNR when the cooperating
nodes are close together. Moreover, whereas cooperation provides no capacity gain in
a static channel without CSIT, in a fading channel transmitter cooperation achieves
a superior capacity than the non-cooperative scheme. In a fading channel, however,
capacity becomes more sensitive to power allocation, and the cooperating nodes need to
be closer together in order for the decode-and-forward transmitter cooperation scheme
to achieve capacity.
Cooperation is beneficial in a fading channel without CSIT, in contrast to an
AWGN channel. However, nodes need to be closer together for decode and
Forward to be capacity achieving.
Also, equal power allocation between transmitter and relay is optimal in fading.
RX2
Optimal cooperation coupled with access and routing

9. Relative Benefits of TX 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. 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

11. 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
Rx co-op
Tx co-op
No co-op

12. 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

13. 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

14. 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.

15. 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

16. 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.

17. 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

18. Iterative vs. One-shot Conferencing
One-shot: DF vs. CF
Iterative vs. One-shot
Weak relay channel: the iterative scheme is disadvantageous.
Strong relay channel: iterative outperforms one-shot conferencing for large C.

19. 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.

20. 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,

21. Routing on the Network Layer
message W1 W2
source 1
destination 1
relay
message W2 W1
source 2
destination 2
This setting still implies routing on the network layer
Relay switches between forwarding two data streams

22. Network Coding Combining data streams on the relay is crucial
source 1
destination 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

23. Wireless Network Coding
TX1
TX2
relay
RX2
RX1 X1 X2
Y3=X1+X2+Z3
Y4=X1+X2+X3+Z4
Y5=X1+X2+X3+Z5
X3= f(Y3)
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.

24. Generalized Relaying Relay can forward all or part of the messages
TX1
TX2
relay
RX2
RX1 X1 X2
Y3=X1+X2+Z3
Y4=X1+X2+X3+Z4
Y5=X1+X2+X3+Z5
X3= f(Y3)
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

25. Beneficial to forward both interference and message

26. Achievable Rates with Simple Network CodingPs P1 P2 P3 P4
Transmitted at the relay:
Received at destination t:
X3=αY3
Compound MAC
Capacity region of Compound MAC is known [Ahslwede,1974]
Achievable rate region for the considered channel
Assumption: No delay

27. Simple scheme achieves capacityPs S D P2 P4
For large powers Ps, P1, P2, analog network coding approaches capacity
Gerard’s talk will discuss practical wireless network coding

28. 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

29. 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

30. 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