Capacity Limits and Cross-Layer
Design in Cooperative Communications
Andrea Goldsmith
Stanford University
WICAT Workshop on
Cooperative Communications
Brooklyn Polytechnic
October 21, 2005
Cooperative/Virtual MIMO
z Nodes
●
Form a multiple-antenna transmitter
z Nodes
●
close together can cooperatively transmit
close together can cooperatively receive
Form a multiple-antenna receiver
z Node
cooperation can increase capacity, save
energy, and reduce delay.
Capacity Gain with
Cooperation (2x2)
x
TX11
G
G
x2
Joint work with N. Jindal
and U. Mitra
z
z
TX cooperation needs large cooperative channel
gain to approach broadcast channel bound
MIMO bound unapproachable
Capacity Gain
vs Network Topology
x1
TX1
x2
d=r<1
x1
Cooperative DPC best
d=1
y2
Joint work with C. Ng
Cooperative
DPC worst
RX2
Optimal cooperation coupled with access and routing
Relative Benefits of
TX and RX Cooperation
z
Two possible CSI models:
z
z
z
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.
z Equal power allocation (a = ½).
Joint work with C. Ng
z
Capacity Evaluation
z
Cut-set upper bound for TX or RX cooperation
z
Decode-and-forward approach for TX cooperation
z
z
Best known achievable rate when RX and relay close
Compress and forward approach for RX cooperation
z
Best known achievable rate when Rx and relay close
Example 1: Optimal power
allocation with full CSI
z
Cut-set bounds
are equal.
z
Tx co-op rate is
close to the
bounds.
z
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
z
z
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
Summary of Results
z
Best cooperation strategy depends on CSI, topology, and
power adaptation.
z Tx co-op is best with full CSI and power adaptation
z RX co-op best with power optimization and receiver
phase CSI
z No capacity gains from cooperation under fixed power
and receiver phase CSI
z
In Tx cooperation power allocation is not essential, but full
CSI (synchronous-carrier) is necessary.
z
In Rx cooperation only receiver CSI (asynchronous-carrier)
is utilized, but optimal power allocation is required.
Multiple-Antenna Relay Channel
z
z
z
z
Full CSI
Power per transmit antenna: P/M.
Single-antenna source and relay
Two-antenna destination
z
z
SNR < PL: MIMO Gain
SNR > PU: No multiplexing gain;
can’t exceed SIMO channel capacity
Cross-Layer Design in
Cooperative Systems
z
Cross-layer design entails joint
design across protocol layers
z
Can result in significant gains in
throughput, efficiency, and QoS.
z
Cross-layer cooperation can take
many forms
z
Most compelling across all layers
of the protocol stack
Protocol Stack
Application
Network
Access
Link
Hardware
Energy-Constrained Nodes
z
Each node can only send a finite number of bits.
z
TX energy minimized by sending each bit very slowly.
z
z
z
Introduces a delay versus energy tradeoff for each bit.
Complicates multiple access
Short-range networks must consider both transmit and
processing/circuit energy.
Sophisticated techniques not necessarily energy-efficient.
z Tradeoffs between TX power and transmission time.
z
z
Changes everything about the network design:
z
z
z
Energy allocation must be optimized across all protocol layers.
Delay vs. throughput vs. node/network lifetime tradeoffs.
Node cooperation must be optimized relative to energy.
Cross-Layer
Optimization Model
Min
s.t.
f 0 ( x1 , x2 ,...)
f i ( x1 , x2 ,...) ≤ 0, i = 1, ", M
g j ( x1 , x2 ,...) = 0, j = 1,", K
z
The cost function f0(.) is energy consumption.
z
The design variables (x1,x2,…) are parameters that
affect energy consumption, e.g. transmission time.
z
fi(x1,x2,…)≤0 and gj(x1,x2,…)=0 are system constraints,
such as a delay or rate constraints.
z
If not convex, relaxation methods can be used.
z
We focus on time division systems
Joint work with S. Cui
Cross-Layer Design to
Minimize Energy
z
Jointly optimize link, MAC, and routing
0.1
Red: hub node
Green: relay/source
0.085
4
(0,0)
3
0.185
(5,0)
0.515
2
(10,0)
0.115
1
(15,0)
R1 = 60 pps
R2 = 80 pps
R3 = 20 pps
• Optimal routing uses single and multiple hops
• Link adaptation yields additional 70% energy savings
Virtual MIMO with Routing
Double String Topology with
Alamouti Cooperation
z
Alamouti 2x1 diversity coding scheme
z
z
z
At layer j, node i acts as ith antenna
Synchronization needed, but no cluster communication
Optimize link design (constellation size); MAC
(transmission time), routing (which hops to use)
Goal is to optimize energy/delay tradeoff curve
Total Energy versus Delay
(with rate adaptation)
Cooperative Compression
z
Source data correlated in space and time
z
Nodes should cooperate in compression as well
as communication and routing
z
Joint source/channel/network coding
z
What is optimal: virtual MIMO vs. relaying
Diversity/Multiplexing
Tradeoffs
z
Use antennas for multiplexing:
High-Rate
Quantizer
ST Code
High Rate
Joint with T. Holliday
Decoder
Error Prone
z
Use antennas for diversity
Low-Rate
Quantizer
ST Code
High
Diversity
Decoder
Low Pe
How should antennas be used? Depends on end-to-end metric.
Optimal Use of Antennas
(Standard MIMO)
z
Can this be extended to cooperative systems?
z
z
Need diversity-multiplexing tradeoff curve
Need end-to-end metric to optimize for
Energy-efficient estimation
σ2
θ (t )
1
σ2
Sensor 1
2
Sensor 2
P1
P2
Joint work with S. Cui,
T. Luo, H.V. Poor
g1
g2
gK
Different observation
quality (known)
z
σ2K
PK
Fusion Center
E (θˆ − θ ) 2 ≤ D0
Different channel
gains (known)
Sensor K
We know little about optimizing this system
z Analog versus digital
z Analog techniques (compression, multiple access)
z Should sensors cooperate in compression/transmission
z Transmit power optimization
Digital v.s. Analog
Conclusions
z
Optimal form of cooperation highly dependent on CSI
assumptions, number of antennas, and network topology.
z
Cooperative communication is inherently a cross-layer
problem.
z
Frameworks to study joint source/channel/network
coding are needed.
z
Diversity/multiplexing tradeoffs in cooperative systems
are not well-understood.
z
Analog communications are making a comeback in
cooperative schemes