capacity, cooperation, and cross-layer design in wireless networks andrea goldsmith stanford...
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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