Capacity, cooperation, and cross-layer
design in wireless networks
Andrea Goldsmith
Stanford University
Conference on Information
Sciences and Systems
Princeton
March 24, 2006
1966
Late 1970s
1st CISS: 1967
Future Wireless Networks
Distributed Sensing, Control, and Communications
Nth Generation Cellular
Nth Generation WLANs
Wireless Ad Hoc Networks
Sensor Networks
Automated Highways
Industrial Automation
Smart Homes/Appliances
•Hard Delay Constraints
•Hard Energy Constraints
•End-to-End Metrics
Challenges

Fundamental capacity limits of wireless networks are
unknown and, worse yet, poorly defined.

Wireless network protocols are generally ad-hoc

Applications are heterogeneous with hard constraints that
must be met by the network

Energy and delay constraints change fundamental design
principles
Fundamental Network Capacity
The Shangri-La of Information Theory

Much progress in finding the capacity limits of
wireless single and multiuser channels

Limited understanding about the capacity limits of
wireless networks, even for simple models

System assumptions such as constrained energy
and delay may require new capacity definitions

Is this elusive goal the right thing to pursue?
Shangri-La is synonymous with any earthly paradise;
a permanently happy land, isolated from the outside world
Network Capacity:
What is it?

n(n-1)-dimensional region
 Rates between all node
 Upper/lower bounds

Other axes
 Energy
and delay
Upper Bound
pairs
Lower bounds achievable
 Upper bounds hard

R34
Lower Bound
R12
Capacity
Upper Bound
Delay
Lower Bound
Energy
Some capacity questions

How to parameterize the region





Power/bandwidth
Channel models and CSI
Outage probability
Security/robustness
Defining capacity in terms of asymptotically small
error and infinite delay has been highly enabling

Has also been limiting


Cause of unconsummated union in networks and IT
What is the alternative?
Network Capacity Results

Multiple access channel (MAC)

Broadcast channel
Gallager
Cover & Bergmans

Relay channel upper/lower bounds

Strong interference channel

Scaling laws

Achievable rates for small networks
Cover &
El Gamal
Sato, Han &
Kobayashi
Gupta & Kumar
Achievable Region Slice
(6 Node Network)
Rij  0, ij  12,34, i  j
Multiple
hops
Spatial
reuse
SIC
(a): Single hop, no simultaneous
transmissions.
(b): Multihop, no simultaneous
transmissions.
(c): Multihop, simultaneous
transmissions.
(d): Adding power control
(e): Successive IC, no power
control.
Joint work with S. Toumpis
Is a capacity region all we
need to design networks?
Yes, if the application and network design can be decoupled
Application metric: f(C,D,E): (C*,D*,E*)=arg max f(C,D,E)
Capacity
(C*,D*,E*)
Delay
Energy
Cooperation in
Ad-Hoc Networks




Peer-to-peer communications.
Fully connected with different time-varying link SINRs
No centralized control
Nodes cooperate to forward data
 Relaying, virtual MIMO, network coding, and conferencing
“We must, indeed, all hang together or, most assuredly,
we shall all hang separately,” Benjamin Franklin
Virtual MIMO
TX1
RX1
TX2
RX2
• 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
Capacity Gain with
Cooperation (2x2)
x
TX11
G
G
x2
Joint work with N. Jindal
and U. Mitra


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

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).
Joint work with C. Ng
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
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.
Multiple-Antenna Relay Channel




Full CSI
Power per transmit antenna: P/M.
Single-antenna source and relay
Two-antenna destination


SNR < PL: MIMO Gain
SNR > PU: No multiplexing gain;
can’t exceed SIMO channel capacity
(Host-Madsen’05)
Joint work with C. Ng and N. Laneman
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 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.
Capacity: Non-orthogonal
Relay Channel



Compare rates to a
full-duplex relay
channel.
Non-orthogonal
Cut-set bound
Realize conference
links via time-division.
Non-orthogonal
CF rate
Orthogonal scheme
suffers a considerable
performance loss,
which is aggravated as
SNR increases.
Non-orthogonal
DF rate
Iterative conferencing
via time-division
Lessons Learned

Orthogonalization has considerable capacity loss


DF vs. CF




Applicable for clusters, since cooperation band can be
reused spatially.
DF: nearly optimal when transmitter and relay are
close (Kramer et. Al.)
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.
Extensions

Partial CSI
 How
to exploit cooperation when you don’t
know CSI?
 Cooperation may not help (Jafar’05)
 Layering: hedge your bets (Shamai’97)

Partial Decoding


We have no relaying schemes under partial decoding
Key to relaying under delay constraints
Crosslayer Design in Ad-Hoc
Wireless Networks

Application

Network

Access

Link

Hardware
Substantial gains in throughput, efficiency, and
end-to-end performance from cross-layer design
Cross-Layer
Design Applications

Joint source/channel coding in MIMO
channels and networks

Energy-constrained networks

Distributed control over wireless networks
Joint Compression and
Channel Coding with MIMO

Use antennas for multiplexing:
High-Rate
Quantizer
ST Code
High Rate
Joint with T. Holliday
Decoder
Error Prone

Use antennas for diversity
Low-Rate
Quantizer
ST Code
High
Diversity
Decoder
Low Pe
How should antennas be used?
Diversity/Multiplexing Tradeoffs
Insert picture
• Where do we operate on this curve?
• Depends on higher-layer metrics
End-to-End Tradeoffs
uR
k
Source
Encoder
s bits
i
Increased rate here
decreases source distortion
Index
Assignment
s bits
p(i)
But permits less
diversity here
Channel
Encoder
MIMO
Channel
A joint design is needed
vj
Source
Decoder
s bits Inverse Index s bits
Assignment
j
p(j)
And maybe higher total distortion
Channel
Decoder
Resulting in more errors
Antenna Assignment vs. SNR
Diversity-Multiplexing-ARQ

Suppose we allow ARQ with incremental redundancy
d 16
14
12
L=4
10
8
6
ARQ Window
4
Size L=1
L=2
L=3
2
0
0

1
2
3
4
r
ARQ is a form of diversity [Caire/El Gamal 2005]
System Model
MIMO-ARQ Channel
Poisson Arrivals
Finite Buffer
Source
Encoder
u Rk
M/G/1 Queue

Arriving data have deadlines

Errors result from ARQ failure or deadline
expiration

What is the optimal tradeoff ?
Joint with T. Holliday and V. Poor
Numerical Results

Distortion for fixed and adaptive schemes
Delay/Throughput/Robustness
across Multiple Layers
B
A

Multiple routes through the network can be used
for multiplexing or reduced delay/loss

Application can use single-description or
multiple description codes

Can optimize optimal operating point for these
tradeoffs to minimize distortion
Cross-layer protocol design
for real-time media
Loss-resilient
source coding
and packetization
Application layer
Rate-distortion preamble
Traffic flows
Congestion-distortion
optimized
scheduling
Transport layer
Congestion-distortion
optimized
routing
Network layer
Capacity
assignment
for multiple service
classes
Link capacities
MAC layer
Link state information
Joint with T. Yoo, E. Setton,
X. Zhu, and B. Girod
Adaptive
link layer
techniques
Link layer
Video streaming
performance
s
5 dB
3-fold increase
100
1000 (logarithmic scale)
Energy-Constrained Nodes

Each node can only send a finite number of bits.



Short-range networks must consider both transmit
and processing/circuit energy.



Energy minimized by sending each bit very slowly.
Introduces a delay versus energy tradeoff for each bit.
Sophisticated techniques not necessarily energy-efficient.
Sleep modes can save energy but complicate networking.
Changes everything about the network design:



Bit allocation must be optimized across all protocols.
Delay vs. throughput vs. node/network lifetime tradeoffs.
Optimization of node cooperation.
Cross-Layer Tradeoffs
under Energy Constraints

Hardware




Link



High-level modulation costs transmit energy but saves
circuit energy (shorter transmission time)
Coding costs circuit energy but saves transmit energy
Access



Models for circuit energy consumption highly variable
All nodes have transmit, sleep, and transient modes
Short distance transmissions require TD optimization
Transmission time (TD) for all nodes jointly optimized
Adaptive modulation adds another degree of freedom
Routing:

Circuit energy costs can preclude multihop routing
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

The cost function f0(.) is energy consumption.

The design variables (x1,x2,…) are parameters that
affect energy consumption, e.g. transmission time.

fi(x1,x2,…)0 and gj(x1,x2,…)=0 are system constraints,
such as a delay or rate constraints.

If not convex, relaxation methods can be used.

We focus on TD systems
Joint work with S. Cui
Minimum Energy Routing

Transmission and Circuit Energy
Red: hub node
Blue: relay only
Green: relay/source
0.3
4
(0,0)
3
(5,0)
2
(10,0)
1
(15,0)
R1  60 pps
R2  R3  0
  100bits
Multihop routing may not be optimal when
circuit energy consumption is considered
Relay Nodes with
Data to Send

Transmission energy only
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

Alamouti 2x1 diversity coding scheme



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

Source data correlated in space and time

Nodes should cooperate in compression as well
as communication and routing

Joint source/channel/network coding

What is optimal: virtual MIMO vs. relaying
Energy-efficient estimation
s2
 (t )
1
s2
Sensor 1
2
Sensor 2
P1
P2
Joint work with S. Cui,
T. Luo, H.V. Poor
g1
g2
gK
Different observation
quality (known)

s 2K
PK
Fusion Center
E (ˆ   ) 2  D0
Different channel
gains (known)
Sensor K
We know little about optimizing this system
 Analog versus digital
 Analog techniques (compression, multiple access)
 Should sensors cooperate in compression/transmission
 Transmit power optimization
Digital v.s. Analog
Distributed Control over
Wireless Links
Joint work
With X. Liu

Packet loss and/or delays impacts controller performance
 There is little methodology to characterize this impact
 Controller sampling determines data rate requirements
 Network design and resulting tradeoffs of rate vs. loss
and delay should be optimized for the controller
Optimal Controller under
Packet Losses
Shared x
Channel 1
l1
Lossy
Channel
Disturbance
x2
Lossy
Channel
Optimal State
Estimator
System
l2
Lossy
Channel
l3
Control Command
State Estimate
State Feedback
Controller
• This structure is optimal for LQG control with no losses.
• Under lossy observations, prove that the optimal controller
is a modified Kalman filter and state feedback controller.
• The controller adapts to packet delay and loss, and its
error covariance is stochastic
• System stability depends on l1, l2, and l3
• These throughput parameters depend on the network design.
Cross-Layer Design
of Distributed Control
Application layer
Network layer
Controller parameters: performance
index, sample period, controller design, etc.
Routing, flow control, etc.
MAC layer
Bandwidth sharing through Medium Access
Physical layer
Modulation, coding, etc.
•Network
design tradeoffs (throughput, delay, loss)
•implicit in the control performance index
Multiple System Example
•
•
•
Inverted Pendulum on a cart.
Two identical systems share the network.
Different weight matrices in the objective function.


Actuator
Actuator
disturbance
u
Control force
disturbance
Cart
Cart
x (position)
Discrete Time
Controller
x (position)
Discrete Time
Controller
Link Layer Design Tradeoffs
(modulation, coding)
Uncoded
BPSK is
optimal!
Iterative Cross Layer Design Example
Optimal vs. Heuristic Controller
Codebook Modulation Heuristic
Optimal
(7,7)
BPSK
7.03
6.77
(15,15)
BPSK

5.77
(31,16)
BPSK

5.84
(31,11)
BPSK

5.91
(31,16)
QPSK
5.88
5.53
(31,11)
QPSK
5.72
5.52
To Cross or not to Cross?

With cross-layering there is higher complexity and
less insight.

Can we get simple solutions or theorems?




What asymptotics make sense in this setting?
Is separation optimal across some layers?
If not, can we consummate the marriage across them?
Burning the candle at both ends


We have little insight into cross-layer design.
Insight lies in theorems, analysis (elegant and dirty),
simulations, and real designs.
Conclusions

Capacity of wireless networks should be better defined

Cooperation in wireless networks is essential – we need to
be more creative about cooperation mechanisms

Frameworks to study joint source/channel/network
coding are needed.

Diversity/multiplexing tradeoffs in cooperative systems
are not well-understood.

End-to-end performance requires a cross-layer design that
exploits tradeoffs at each layer by higher layer protocols