EE360: Lecture 9 Outline

1. 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

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 RX1 RX2 TX2

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. 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

7. 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.

8. 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

9. 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. 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 Tx co-op Rx 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 • 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

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 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

22. 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

23. 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.

24. 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

25. Beneficial to forward bothinterference and message

26. 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

27. 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

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 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