Capacity, cooperation, and cross-layer design in wireless networks Andrea Goldsmith Stanford University Conference on Information Sciences and Systems Princeton March 24, 2006

Late 1970s st CISS: 1967

Future Wireless Networks Nth Generation Cellular Nth Generation WLANs Wireless Ad Hoc Networks Sensor Networks Automated Highways Industrial Automation Smart 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 pairs Upper/lower bounds l Lower bounds achievable l Upper bounds hard Other axes Energy and delay R 12 R 34 Upper Bound Lower Bound Capacity Delay Energy Upper Bound Lower Bound

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 l 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. Multiple hops 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 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 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 TX1 x1x1 x2x2 GG Joint work with N. Jindal and U. Mitra

Capacity Gain vs Network Topology Cooperative DPC best Cooperative DPC worst RX2 y2y2 TX1 x1x1 x2x2 x1x1 d=1 d=r<1 Joint work with C. Ng 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

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 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-op Rx 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 < P L : MIMO Gain SNR > P U : 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. CFIterative 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-orthogonal CF rate Non-orthogonal DF rate Non-orthogonal Cut-set bound Iterative conferencing via time-division

Lessons Learned Orthogonalization has considerable capacity loss Applicable for clusters, since cooperation band can be reused spatially. DF vs. CF 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: Use antennas for diversity High-Rate Quantizer ST Code High Rate Decoder Error Prone Low P e Low-Rate Quantizer ST Code High Diversity Decoder 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 Index Assignment s bits  i) Channel Encoder s bits i MIMO Channel Channel Decoder Inverse Index Assignment  j) s bits j Increased rate here decreases source distortion But permits less diversity here Resulting in more errors Source Encoder Source Decoder And maybe higher total distortion A joint design is needed vjvj

Antenna Assignment vs. SNR

Diversity-Multiplexing-ARQ Suppose we allow ARQ with incremental redundancy ARQ is a form of diversity [Caire/El Gamal 2005] ARQ Window Size L=1 L=2L=3 L=4

System Model Arriving data have deadlines Errors result from ARQ failure or deadline expiration What is the optimal tradeoff? Poisson Arrivals Finite Buffer MIMO-ARQ Channel 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 Congestion-distortion optimized routing Congestion-distortion optimized routing Adaptive link layer techniques Adaptive link layer techniques Loss-resilient source coding and packetization Congestion-distortion optimized scheduling Congestion-distortion optimized 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 Hardware Models for circuit energy consumption highly variable All nodes have transmit, sleep, and transient modes Short distance transmissions require TD optimization Link High-level modulation costs transmit energy but saves circuit energy (shorter transmission time) Coding costs circuit energy but saves transmit energy Access 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 The cost function f 0 (.) is energy consumption. The design variables (x 1,x 2,…) are parameters that affect energy consumption, e.g. transmission time. f i (x 1,x 2,…)  0 and g j (x 1,x 2,…)=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 s.t. Joint work with S. Cui

Minimum Energy Routing Transmission and Circuit Energy (0,0) (5,0)(10,0) (15,0) Multihop routing may not be optimal when circuit energy consumption is considered Red: hub node Blue: relay only Green: relay/source

Relay Nodes with Data to Send Transmission energy only Red: hub node Green: relay/source (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 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 We know little about optimizing this system Analog versus digital Analog techniques (compression, multiple access) Should sensors cooperate in compression/transmission Transmit power optimization Sensor 1 Sensor 2 Sensor K Fusion Center Different channel gains (known) Different observation quality (known) g1g1 g2g2 gKgK 2121 2222 2K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 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 performance Joint work With 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 State Estimator State Feedback Controller State Estimate Control Command Disturbance x1x1 Lossy Channel Lossy Channel x2x2 Optimal Controller under Packet Losses Lossy Channel Shared Channel 1 2 3

Cross-Layer Design of 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. u Control force Cart x (position)  disturbance Discrete Time Controller Actuator Cart x (position)  disturbance Discrete Time Controller Actuator

Link Layer Design Tradeoffs (modulation, coding) Uncoded BPSK is optimal!

Iterative Cross Layer Design Example

Optimal vs. Heuristic Controller CodebookModulationHeuristicOptimal (7,7)BPSK (15,15)BPSK5.77 (31,16)BPSK5.84 (31,11)BPSK5.91 (31,16)QPSK (31,11)QPSK   

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