Robust Mulilayer Design of Wireless Networks for Distributed Systems

1. Robust Mulilayer Design of Wireless Networks for Distributed Systems Andrea Goldsmith Stanford University wsl.stanford.edu IPAM Workshop May 16, 2002

2. Massively Distributed Systems

3. Challenges • Design and capacity of large wireless adhoc networks are open problems • Hard energy and delay constraints change fundamental design principles • Many applications fail miserably with a “generic” network approach

4. Example: String Stability • Applied to vehicle platoons with linear controllers • String stable if spacing error decreases along platoon • Communication system: token passing WLAN • Controllers unstable for any delay in lead vehicle information • Lead vehicle broadcasts or controller redesign stabilizes the system under bounded delay

5. Multilayer Design Multilayer Design • Hardware • Power or hard energy constraints • Size constraints • Link Design • Time-varying low capacity channel • Multiple Access • Resource allocation (power, rate, BW) • Interference management • Networking. • Routing, prioritization, and congestion control • Application • Real time media and QOS support • Hard delay/quality constraints

6. Design Issues • Some applications require tight coupling across layers, while others can be more flexible • Diversity and adaptability are essential for robustness • What information should be exchanged across layers and how it should be used

7. Outline • Fundamental capacity limits • Adaptive modulation and resource allocation • Medium access control • Ad hoc network design • Energy constrained networks • Joint control and communication design • Multilayer network design

8. Broadcast: One Transmitter to Many Receivers. Multiple Access: Many Transmitters to One Receiver. Wireless Channel CapacityFundamental Limit on Data Rates Capacity: The set of simultaneously achievable rates {R1,…,Rn} • Main drivers of channel capacity • Bandwidth and power • Statistics of the channel • Channel knowledge at transmitter/receiver • Number of antennas • Minimum rate and delay constraints R3 R2 R1

9. Min-Rate Capacity Region: Severe Rician Fading P = 10 mW, B = 100 KHz Independent Rician fading with K=1 for both users (severe fading, but not as bad as Rayleigh).

10. M(g)-QAM Modulator Power: S(g) Point Selector Uncoded Data Bits One of the M(g) Points log2 M(g) Bits Adaptive Modulation and Coding in Flat Fading • Adapt transmission to channel • Parameters: power,rate,code,BER, etc. • Capacity-achieving strategy • Recent Work • Adaptive modulation for voice and data (to meet QOS) • Adaptive turbo coded modulation (<1 db from capacity) • Multiple degrees of freedom (only need exploit 1-2) • Adaptive power, rate, and compression with hard deadlines Buffer To Channel g(t) g(t) 16-QAM 4-QAM BSPK

11. Adaptation under Hard Delay Constraints  Optimal Power Control and Joint Source/Channel Coding Power (mW) 30ms constraint 90ms constraint Data Rate (bps)

12. Ad-Hoc Network Capacity • Each node generates independent data. • Source-destination pairs are chosen at random. • Routing can be multihop. • Topology is dynamic • Generally a fully connected network with different link SNRs • Can allocate resources dynamically (rate, power, BW, routes,…)

13. 2 3 5 4 1 Capacity Region • All achievable rate vectors between nodes • An n(n-1) dimensional convex polyhedron • Each dimension defines (net) rate from one node to each of the others • Achievability • Time division • AWGN or flat fading • Centralized control • Converse

14. Rate Matrix • Transmission scheme at time t for n users (snapshot) • Rows represent original data source • Negative entries represent bits to send or forward • Positive entries represent bits received (data rate) • Link rates dictated by link capacity given SIR (variable rate) • Multihop routing and power control increase set of matrices Transmission Scheme Rate Matrix 1 2 Data from 1, rate 10 4 3 Data from 2, rate 20

15. Time Division • Time division of two schemes is a linear combination of their rate matrices. • Example: 50% of time under scheme A and 50% of time under scheme B has rate matrix: Scheme A Scheme B 50/50 Time Division User 1 sends 5 bps/Hz to User 2 User 2 sends 10 bps/Hz to User 3 and 10 bps/Hz to User 4 User 4 sends 5 bps/Hz to User 3

16. Achievable rate vectors achieved by time division Capacity region is convex hull of all rate matrices Capacity Region • A matrix R belongs to the capacity region if there are rate matrices R1, R2, R3 ,…, Rn such that • Linear programming problem: • Need clever techniques to reduce complexity • Power control, fading, etc., easily incorporated • Region boundary achieved with optimal routing

17. Example: Six Node Network Capacity region is 30-dimensional

18. Capacity Regions (a): Single hop, no simultaneous transmissions. (b): Multihop, no simultaneous transmissions. (c): Multihop, simultaneous transmissions. (d): Adding power control (e): Successive interference cancellation, no power control. Multiple hops SIC Spatial reuse Extensions: - Capacity vs. network size - Energy constraints - Fading and mobility - Multihop cellular

19. Fading increases capacity • Gain matrix alternates between N fading states • In a similar way, mobility also increases capacity (a): No routing, no simultaneous transmissions. (b): Routing, no simultaneous transmissions. (c): Routing, simultaneous transmissions. (d): Adding power control. (e): Successive interference cancellation, no power control.

20. Relay transmissions S Sc Xi Yk Xk Yj Nodes can transmit directly and/or use other nodes as relays Shannon Capacity of Ad-Hoc Networks • For n nodes,  p(x(1),…,x(n)) s.t.(Cover/Thomas) Rate flow across cutsets bounded by conditional MI

21. Relay Channel Results • Direct plus one relay (Cover,El Gamal’79) • Parallel relays (Schein,Gallager’00) N2 • Capacity Strategy: • - Broadcast coding • Cooperative MAC coding • Source coding • Random, list, block Markov codes Destination Source + + N1 • Capacity Upper Bounds • 1) Data processing thm • 2) Cover/El Gamal result • Achievability • 1) Staggered block coding • 2) Transponder scheme N3 N2 + Destination Source + + N1 Bounds not tight: hard problem

22. Capacity Ideas for Ad Hoc Networks • Multiple Antenna (MIMO) Channels • Can obtain large capacity increases with multiple antennas • In sensor networks, sensor clusters can utilize these gains • Interference • “Dirty paper” coding removes the effect of known interference without increasing required transmit power

23. Random Access • Shannon capacity ignores data arrival statistics • Does MAC capacity change for bursty data? • Can only decrease • Need better transmission strategies for Aloha • Need better methods of collision resolution

24. Hidden Terminal Exposed Terminal 1 2 3 4 5 Medium Access Control • Nodes need a protocol for channel access • Minimize packet collisions and insure channel not wasted • Collisions entail significant delay • First protocols designed for fully-connected networks • Suffer from hidden and exposed terminal problems • 802.11 uses four-way handshake • Creates inefficiencies, especially in multihop setting

25. Multiple mini-slots mini-slot pairs data slot • Multiple mini-slots increase efficiency of collision resolution • Different minislot protocols investigated • Distributed p-Persistent Algorithm (DPA) • Distributed Splitting Algorithm (DSA) • Distributed Token Bus (DTB) • Propagation delay factored in guard times • Non FIFO queueing also improves efficiency Time

26. Throughput versus Delay (f) (b) (a): Theoretical bound (b): IEEE802.11 upper bound (c): IEEE802.11 (d): DPA (d’): non-FIFO DPA (e): DSA (e’): non-FIFO DSA (f): DPA (f’): non-FIFO DPA (a) (e) (c) (d’) (d) (f’) (e’) Numerical results obtained via discrete event simulation

27. DTB Capacity Region (a): Theoretical bound (b): IEEE802.11 upper bound (c): IEEE802.11 (d): DPA (e): DSA (f): DPA (f) (a) (e) (b) (c) (d)

28. MAC with Data Prioritization l2=p2L/T • Each user transmits whenever he has data to send • Coding strategy: Combine broadcast and MAC • Each user sends a multiresolution signal • Without collisions all data gets through • With collisions some data gets through • Lost bits may be retransmitted l1=p1L/T

29. Results • High priority data always gets through • This coding strategy achieves capacity • If (l1,l2)C, these rates will be achieved • Burstiness does not decrease capacity! • Superposition coding only needed when users have very different SNRs • Otherwise code for constant collisions or no collisions, depending on pi. • Show that queues in system are stable for any rate pair (l1,l2) inside MAC capacity region.

30. Networks with Energy-Constrained Nodes • Capacity per unit energy (Gallager’87, Verdu’90) • Number of bits per unit energy such that error probability decreases to zero with increasing energy • Not possible to send a finite number of bits with finite energy and Pe arbitrarily small • Energy per bit minimized by sending bits over many dimensions (symbols,time,BW) • New communication system paradigm • Network designs must now consider node lifetime (among other things) in MAC and routing protocols

31. Energy Constrained Networks • Channel capacity is the maximum possible rate with arbitrarily small Pe (reliable transmission) • Input often has an average or peak power constraint • Capacity per unit cost (Gallager’87, Verdu’90) • Number of bits that can be transmitted per unit cost for sending these bits (cost is typically energy) • Not possible to send a finite number of bits with finite energy and Pe arbitrarily small • Capacity per unit energy achieved with on-off signalling • We investigate dynamic rate, power, and routing strategies for networks with finite-energy nodes

32. Bits per Unit Energy • General channels with a “0” (Verdu’90) • Gaussian channels with energy E and M messages • Minimum energy per bit: • Codes arbitrarily long for small Pe,and E

33. Energy vs. Symbol per Bit Energy/bit N0 ln2 Symbols/bit Minimum energy per bit achieved with many degrees of freedom

34. Can fading help? • For most fading distributions, channel gain is large with small probability • With finite energy, can transmit any number of bits with Pe arbitrarily small • Transmit when channel is “good” • Delay can be large • Capacity per unit energy typically infinite • We consider maximizing the number of bits transmitted reliably over a block fading channel • Delay constraint: can’t average over all fading values

35. System Model • m blocks of n symbols (n large) • m represents delay constraint • Each block has small but nonzero Pe • Fading gain on ith block is g[i] (i.i.d.) • Transmitter and receiver know g[i] at time i • Energy on ith block: • Effective energy on ith block: X11,…,X1n X21,…,X2n Xm1,…,Xmn g1 g2 gm

36. Maximizing Transmitted Bits • AWGN channel with gain g and energy E: • Minimum energy per bit: N0 ln 2/g • Bits per unit energy: g/(N0 ln 2) • Total number of bits sent: B=gE/(N0 ln 2) • For block fading, bits sent in ith frame: Goal: optimally allocate E to maximize sum of bits

37. Problem Formulation • Optimizing Energy Allocation • Finite horizon dynamic programming • Value iteration algorithm

38. Threshold Policy • Energy allocated according to threshold rule • Recursion for ai: • Threshold decreases with each block: aiai+1 Use all energy in current block if fading exceeds expected future gains

39. Threshold Level Threshold Level in Rayleigh Fading for m=20 3.5 3 Transmit 2.5 2 Threshold ai 1.5 Don’t Transmit 1 0.5 0 0 2 4 6 8 10 12 14 16 18 20 Block Number

40. Capacity Evaluation • Maximum number of transmitted bits

41. 10 20 30 Capacity in Rayleigh Fading 15 10 5 0 0 40 50 60 70 80 90 100 Block Number

42. An-1 Energy Constrained Routing • Ad hoc network with n nodes • Link gains between nodes are Gij. • Each node has finite energy Ei • Minimum energy to send 1 bit on link ijis N0ln2/Gij • Maximize the total number of bits sent from A0to An-1given the node energy constraints A0

43. Minimum Energy Routing • Routing strategy for each bit: • Choose a route from A0to An-1 with the minimum total energy per bit (minimum cost) • Shortest path problem • Solved using dynamic programming • Reduce node energy after each transmission • Total number of transmitted bits depends on node energies

45. Joint Control and Network Design • Robust controllers compensate for modeling errors • There is little known about incorporating random packet delays and losses into controller design • Network-robust controllers must compensate for asynchronous, delayed, and lossy information • Network tradeoffs impact controller performance • Rate vs delay, hard deadlines, energy constraints. • Network requirements defined by controller design Network and controller should be jointly designed

46. Fundamental Trade-offs • Effects of communication faults on controller • High data rates, low latency, low packet loss are competing objectives in wireless networks. Control system Data rates Quantization noise Random Packet Delay Delay and asynchronicity in feedback Packet loss Vacant sampling

47. General Problem Setup Noise & disturbance Regulated outputs LTI Plant Sh Hh Sampled outputs Measured outputs Actual control input Wireless Link Wireless Link Remote Controller Desired control input Goal: Investigate effects of quantization noise, packet loss/delay, and link design and adaptation on the controller performance.

48. Performance • We consider both hard and soft decoding on the link • Soft decision implies no packet errors or loss • Hard decision entails random packet loss • H2 norm – the covariance in the regulated output when the driven noise is N(0, I). • Hybrid system (sampled-data system) is not LTI, but it is periodic. We use a generalized H2 norm. • Sampled-data H2 optimal control solved via an associated discrete-time system, which depends on sample period h. • With packet loss, we use the covariance in the regulated output as performance measure. • The regulated output is a Gaussian mixture • Its statistics are time-varying.

49. Robustness to Packet Loss

50. Robustness to Imperfect Communication