Capacity cooperation and cross-layer design in wireless networks

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 1970 s 1 st 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 l Fundamental capacity limits of wireless networks are unknown and, worse yet, poorly defined. l Wireless network protocols are generally ad-hoc l Applications are heterogeneous with hard constraints that must be met by the network l Energy and delay constraints change fundamental design principles

Fundamental Network Capacity The Shangri-La of Information Theory l Much progress in finding the capacity limits of wireless single and multiuser channels l Limited understanding about the capacity limits of wireless networks, even for simple models l System assumptions such as constrained energy and delay may require new capacity definitions l 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? l n(n-1)-dimensional region l Rates between all node pairs l Upper/lower bounds l Lower bounds achievable l Upper bounds hard l Other axes l Energy and delay R 34 Upper Bound Lower Bound R 12 Capacity Upper Bound Delay Lower Bound Energy

Some capacity questions l How to parameterize the region l l l 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 l Has also been limiting l l Cause of unconsummated union in networks and IT What is the alternative?

Network Capacity Results l Multiple access channel (MAC) l Broadcast channel Gallager Cover & Bergmans l Relay channel upper/lower bounds l Strong interference channel l Scaling laws l Achievable rates for small networks Cover & El Gamal Sato, Han & Kobayashi Gupta & Kumar

Achievable Region Slice (6 Node Network) 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 l l Peer-to-peer communications. Fully connected with different time-varying link SINRs No centralized control Nodes cooperate to forward data l Relaying, virtual MIMO, network coding, and conferencing “We must, indeed, all hang together or, most assuredly, we shall hang separately, ” Benjamin Franklin

Virtual MIMO TX 1 RX 1 TX 2 RX 2 • TX 1 sends to RX 1, TX 2 sends to RX 2 • TX 1 and TX 2 cooperation leads to a MIMO BC • RX 1 and RX 2 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 (2 x 2) x TX 11 G G x 2 Joint work with N. Jindal and U. Mitra l l TX cooperation needs large cooperative channel gain to approach broadcast channel bound MIMO bound unapproachable

Capacity Gain vs Network Topology x 1 TX 1 x 2 d=r<1 x 1 Cooperative DPC best d=1 y 2 Joint work with C. Ng Cooperative DPC worst RX 2 Optimal cooperation coupled with access and routing

Relative Benefits of TX and RX Cooperation l Two possible CSI models: l l l 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 a. P, and relay (1 -a)P ; 0≤a≤ 1 needs to be optimized. l Equal power allocation (a = ½). Joint work with C. Ng l

Capacity Evaluation l Cut-set upper bound for TX or RX cooperation l Decode-and-forward approach for TX cooperation l l Best known achievable rate when RX and relay close Compress and forward approach for RX cooperation l Best known achievable rate when Rx and relay close

Example 1: Optimal power allocation with full CSI l Cut-set bounds are equal. l Tx co-op rate is close to the bounds. l 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 l l 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 l Capacity gain only realized with the right cooperation strategy l With full CSI, Tx co-op is superior. l With optimal power allocation and receiver phase CSI, Rx co-op is superior. l With equal power allocation and Rx phase CSI, cooperation offers no capacity gain. l Similar observations in Rayleigh fading channels.

Multiple-Antenna Relay Channel l l Full CSI Power per transmit antenna: P/M. Single-antenna source and relay Two-antenna destination l l 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 l Willems introduced conferencing for MAC (1983) l Transmitters conference before sending message l We consider a relay channel with conferencing between the relay and destination l 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 l Weak relay channel: the iterative scheme is disadvantageous. l Strong relay channel: iterative outperforms one-shot conferencing for large C.

Capacity: Non-orthogonal Relay Channel l Compare rates to a fullduplex relay channel. Realize conference links via time-division. Orthogonal scheme suffers a considerable performance loss, which is aggravated as SNR increases. Non-orthogonal Cut-set bound Non-orthogonal DF rate Non-orthogonal CF rate Iterative conferencing via time-division

Lessons Learned l Orthogonalization has considerable capacity loss l l 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. ) l CF: nearly optimal when transmitter and relay far l CF: not sensitive to compression scheme, but poor spectral efficiency as transmitter and relay do not joint -encode. l l The role of SNR High SNR: rate requirement on cooperation messages increases. l MIMO-gain region: cooperative system performs as well as MIMO system with isotropic inputs. l

Extensions l Partial CSI l How to exploit cooperation when you don’t know CSI? l Cooperation may not help (Jafar’ 05) l Layering: hedge your bets (Shamai’ 97) l Partial Decoding We have no relaying schemes under partial decoding l Key to relaying under delay constraints l

Crosslayer Design in Ad-Hoc Wireless Networks l Application l Network l Access l Link l Hardware Substantial gains in throughput, efficiency, and end-to performance from cross-layer design

Cross-Layer Design Applications l Joint source/channel coding in MIMO channels and networks l Energy-constrained networks l Distributed control over wireless networks

Joint Compression and Channel Coding with MIMO l Use antennas for multiplexing: High-Rate Quantizer ST Code High Rate Joint with T. Holliday Decoder Error Prone l 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 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 l Suppose we allow ARQ with incremental redundancy L=4 ARQ Window L=2 L=3 Size L=1 l ARQ is a form of diversity [Caire/El Gamal 2005]

System Model MIMO-ARQ Channel Poisson Arrivals Finite Buffer Source Encoder M/G/1 Queue l Arriving data have deadlines l Errors result from ARQ failure or deadline expiration l What is the optimal tradeoff? Joint with T. Holliday and V. Poor

Numerical Results l Distortion for fixed and adaptive schemes

Delay/Throughput/Robustness across Multiple Layers B A l Multiple routes through the network can be used for multiplexing or reduced delay/loss l Application can use single-description or multiple description codes l 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 Congestion-distortion optimized scheduling Traffic flows 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 d. B 3 -fold increase 1000 (logarithmic scale)

Energy-Constrained Nodes l Each node can only send a finite number of bits. l l l 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. l Sleep modes can save energy but complicate networking. l l Changes everything about the network design: l l l 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 l Hardware l l 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) l Coding costs circuit energy but saves transmit energy l l Access l l l Transmission time (TD) for all nodes jointly optimized Adaptive modulation adds another degree of freedom Routing: l Circuit energy costs can preclude multihop routing

Cross-Layer Optimization Model Min s. t. l The cost function f 0(. ) is energy consumption. l The design variables (x 1 , x 2, …) are parameters that affect energy consumption, e. g. transmission time. l fi(x 1, x 2, …) 0 and gj(x 1, x 2, …)=0 are system constraints, such as a delay or rate constraints. l If not convex, relaxation methods can be used. l We focus on TD systems Joint work with S. Cui

Minimum Energy Routing l 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) Multihop routing may not be optimal when circuit energy consumption is considered

Relay Nodes with Data to Send l Transmission energy only 0. 1 Red: hub node Green: relay/source 0. 085 4 (0, 0) 3 0. 185 (5, 0) 2 (10, 0) 0. 115 1 (15, 0) 0. 515 • Optimal routing uses single and multiple hops • Link adaptation yields additional 70% energy savings

Virtual MIMO with Routing

Double String Topology with Alamouti Cooperation l Alamouti 2 x 1 diversity coding scheme l l l 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 l Source data correlated in space and time l Nodes should cooperate in compression as well as communication and routing l Joint source/channel/network coding l What is optimal: virtual MIMO vs. relaying

Energy-efficient estimation s 2 1 s 2 Sensor 1 2 Sensor 2 Joint work with S. Cui, T. Luo, H. V. Poor g 1 g 2 g. K Different observation quality (known) l s 2 K Fusion Center Different channel gains (known) Sensor K We know little about optimizing this system l Analog versus digital l Analog techniques (compression, multiple access) l Should sensors cooperate in compression/transmission l Transmit power optimization

Digital v. s. Analog

Distributed Control over Wireless Links Joint work With X. Liu l Packet loss and/or delays impacts controller performance l There is little methodology to characterize this impact l Controller sampling determines data rate requirements l Network design and resulting tradeoffs of rate vs. loss and delay should be optimized for the controller performance

Optimal Controller under Packet Losses Shared x Channel 1 Lossy Channel x 2 Lossy Channel Optimal State Estimator System l 2 Disturbance Lossy Channel l 3 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 l 1, l 2, and l 3 • 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. q q Actuator disturbance u Control force disturbance Cart 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? l With cross-layering there is higher complexity and less insight. l Can we get simple solutions or theorems? l l 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 l l We have little insight into cross-layer design. Insight lies in theorems, analysis (elegant and dirty), simulations, and real designs.

Conclusions l Capacity of wireless networks should be better defined l Cooperation in wireless networks is essential – we need to be more creative about cooperation mechanisms l Frameworks to study joint source/channel/network coding are needed. l Diversity/multiplexing tradeoffs in cooperative systems are not well-understood. l End-to-end performance requires a cross-layer design that exploits tradeoffs at each layer by higher layer protocols