ee360: lecture 9 outline announcements makeup lecture this friday, 2/7, 12-1:15pm in packard 312...
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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
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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,”
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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
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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,”
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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