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

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 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

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

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

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

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 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

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,”

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 Rx co-op Tx 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 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.

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 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

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

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.

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

Beneficial to forward both interference and message

Achievable Rates with Simple Network Coding Ps 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

Simple scheme achieves capacity Ps S D 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 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