Capacity, cooperation, and cross-layer design in wireless

networks

Andrea GoldsmithStanford University

Conference on Information Sciences

and SystemsPrinceton

March 24, 2006

Late 1970s

1966

1st CISS: 1967

Future Wireless Networks

Nth Generation CellularNth Generation WLANsWireless Ad Hoc NetworksSensor Networks Automated HighwaysIndustrial AutomationSmart Homes/Appliances

Distributed Sensing, Control, and Communications

•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 pairsUpper/lower bounds

Lower bounds achievable Upper bounds hard

Other axesEnergy and delay

R12

R34

Upper Bound

Lower Bound

Capacity Delay

Energy

Upper Bound

Lower Bound

Some capacity questions

How to parameterize the regionPower/bandwidthChannel models and CSIOutage probabilitySecurity/robustness

Defining capacity in terms of asymptotically small error and infinite delay has been highly enablingHas also been limiting

Cause of unconsummated union in networks and IT

What is the alternative?

Network Capacity Results

Multiple access channel (MAC)

Broadcast channel

Relay channel upper/lower bounds

Strong interference channel

Scaling laws

Achievable rates for small networks

Gallager

Cover & Bergmans

Cover & El Gamal

Gupta & Kumar

Sato, Han &Kobayashi

Achievable Region Slice

(6 Node Network)

(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.

jiijRij ,34,12 ,0

Multiplehops

Spatial reuse

SIC

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

Capacity

Delay

Energy

Application metric: f(C,D,E): (C*,D*,E*)=arg max f(C,D,E)

(C*,D*,E*)

Cooperation inAd-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 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

Capacity Gain with Cooperation (2x2)

TX cooperation needs large cooperative channel gain to approach broadcast channel bound

MIMO bound unapproachable

TX1x1

x2

GG

Joint work with N. Jindal and U. Mitra

Capacity Gainvs Network Topology

Cooperative DPC best

Cooperative DPC worst

RX2

y2

TX1x1

x2

x1

d=1

d=r<1

Joint work with C. Ng

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).

Joint work with C. Ng

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

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 CSIPower 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

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

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

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 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 SNRHigh SNR: rate requirement on cooperation

messages increases.MIMO-gain region: cooperative system performs

as well as MIMO system with isotropic inputs.

Extensions

Partial CSIHow to exploit cooperation when

you don’t know CSI?Cooperation may not help (Jafar’05)Layering: hedge your bets

(Shamai’97)

Partial DecodingWe have no relaying schemes under

partial decodingKey to relaying under delay constraints

Crosslayer Design in Ad-Hoc Wireless

Networks

ApplicationNetworkAccessLink

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 andChannel Coding with

MIMOUse antennas for multiplexing:

Use antennas for diversity

High-RateQuantizer

ST CodeHigh Rate Decoder

Error Prone

Low Pe

Low-RateQuantizer

ST CodeHigh

DiversityDecoder

How should antennas be used?

Joint with T. Holliday

Diversity/Multiplexing Tradeoffs

Insert picture

• Where do we operate on this curve?• Depends on higher-layer metrics

End-to-End Tradeoffs

kRu Index

Assignment

s bits

i)Channel Encoder

s bits

i

MIMO Channel

Channel Decoder

Inverse Index Assignment j)

s bits

j

s bits

Increased rate heredecreases source

distortion

But permits less diversity

here

Resulting in more errors

SourceEncoder

SourceDecoder

And maybe higher total distortion

A joint design is needed

vj

Antenna Assignment vs. SNR

Diversity-Multiplexing-ARQ

Suppose we allow ARQ with incremental redundancy

ARQ is a form of diversity [Caire/El Gamal 2005]

0

2

4

6

8

10

12

14

16

0 1 2 3 4

ARQ Window

Size L=1

L=2 L=3

L=4

d

r

System Model

Arriving data have deadlines

Errors result from ARQ failure or deadline expiration

What is the optimal tradeoff?

Poisson ArrivalsFinite Buffer

MIMO-ARQ Channel

kRu M/G/1 Queue

Source

Encoder

Joint with T. Holliday and V. Poor

Numerical Results

Distortion for fixed and adaptive schemes

Delay/Throughput/Robustness across

Multiple Layers

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

A

B

Application layer

Network layer

MAC layer

Link layer

Cross-layer protocol design for real-time

media

Capacity assignment

for multiple service classes

Capacity assignment

for multiple service classes

Congestion-distortionoptimizedrouting

Congestion-distortionoptimizedrouting

Adaptivelink layer

techniques

Adaptivelink layer

techniques

Loss-resilientsource coding

and packetization

Loss-resilientsource coding

and packetization

Congestion-distortionoptimized

scheduling

Congestion-distortionoptimized

scheduling

Traffic flows

Link capacities

Link state information

Transport layer

Rate-distortion preamble

Joint with T. Yoo, E. Setton, X. Zhu, and B. Girod

Video streaming performance

3-fold increase

5 dB

100

s

(logarithmic scale)

1000

Energy-Constrained Nodes

Each node can only send a finite number of bits.Energy minimized by sending each bit very slowly. Introduces a delay versus energy tradeoff for each bit.

Short-range networks must consider both transmit and processing/circuit energy.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

HardwareModels for circuit energy consumption highly variableAll nodes have transmit, sleep, and transient modesShort distance transmissions require TD optimization

LinkHigh-level modulation costs transmit energy but saves

circuit energy (shorter transmission time)Coding costs circuit energy but saves transmit energy

AccessTransmission time (TD) for all nodes jointly optimizedAdaptive modulation adds another degree of freedom

Routing:Circuit energy costs can preclude multihop routing

Cross-Layer Optimization Model

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

Min ,...),( 210 xxf

s.t. ,0,...),( 21 xxfi Mi ,,1 Kj ,,1 ,0,...),( 21 xxg j

Joint work with S. Cui

Minimum Energy Routing

Transmission and Circuit Energy

4 3 2 1

0.3

(0,0)

(5,0)

(10,0)

(15,0)

Multihop routing may not be optimal when circuit energy consumption is considered

bits

RR

ppsR

100

0

60

32

1

Red: hub nodeBlue: relay onlyGreen: relay/source

Relay Nodes with Data to Send

Transmission energy only

4 3 2 10.115

0.515

0.185

0.085

0.1Red: hub nodeGreen: relay/source

ppsR

ppsR

ppsR

20

80

60

3

2

1

(0,0)

(5,0)

(10,0)

(15,0)

• 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 schemeAt layer j, node i acts as ith antennaSynchronization 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 codingWhat is optimal: virtual MIMO vs. relaying

Energy-efficient estimation

We know little about optimizing this systemAnalog versus digital Analog techniques (compression, multiple access)Should sensors cooperate in compression/transmissionTransmit power optimization

Sensor 1

Sensor 2

Sensor K

Fusion Center

Different channel gains (known)

Different observation quality (known)

1P

2P

KP

)(t

02)ˆ( DE

g1

g2

gK

21

22

2K

Joint work with S. Cui, T. Luo, H.V. Poor

Digital v.s. Analog

Distributed Control over Wireless Links

Packet loss and/or delays impacts controller performanceThere is little methodology to characterize this impactController sampling determines data rate requirementsNetwork design and resulting tradeoffs of rate vs. loss and delay should be

optimized for the controller performance

Joint workWith X. Liu

• 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 1, 2, and 3

• These throughput parameters depend on the network design.

System

Optimal StateEstimator

State FeedbackController

State Estimate

Control Command

Disturbancex1

LossyChannel

LossyChannel

x2

Optimal Controller under

Packet Losses

LossyChannel

SharedChannel

12

3

Cross-Layer Designof Distributed Control

Application layer

Network layer

Physical layer

MAC layer

Controller parameters: performance index, sample period, controller design, etc.

Routing, flow control, etc.

Bandwidth sharing through Medium Access

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.

uControl force

Cart

x (position)

disturbance

Discrete TimeController

Actuator

Cart

x (position)

disturbance

Discrete TimeController

Actuator

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 endsWe 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