Network-Layer View of Cooperation

1. Network-Layer View of Cooperation Anthony Ephremides University of Maryland MSRI Workshop April 10, 2006 Based on joint work with: R. Liu (UMD), S. Misra (ARL/Cornell U.), A. Sadek (UMD), Y. Sung (Qualcomm), L. Tong (Cornell U.), and L. Yu (UMD)

2. Preview • Cooperation in a Network can occur at different levels • One example at the MAC layer • One example at the Routing layer • Unless and until we break the barriers among layers, considering cooperation in a broader sense is useful

3. A little (but important) Background • Much touted question of ‘‘capacity‘‘ • Maximum Throughput Region (packets/slot) (saturated queues)-TR • Maximum Stable Throughput Region (packets/slot) (finite delays)-STR • Capacity Region (bits/s) (reliable communication limits)-C • TR, STR, C : need not coincide Ad Hoc Wireless Network

4. Example: 2-users in random access collision channel 2 1 1 R TR 2 TR=STR=C Error-free when no collision • “Thorny” model to extend • Interacting Queues-Dominant Systems • No-Cooperation yet! 1 1 STR

5. More General Network • Similar goal= Find TR, STR, C • Gupta & Kumar (2000)=TR (asymptotically) • Tassiulas and Ephremides (1992) (STR) • Tassiulas & Neely & Geo (2006) (STR) • Point-to-point • Scheduled access (mostly) D Based on “back-pressure” algorithm Equalizes queue loads Delay can be substantial (not “routing-savvy”) 1 1

6. 1 2 M i 1st Example-Cooperation at the MAC level • Network view of the relay channel • TDMA underlying structure (i): ith-user’s portion (interference-free) • Success if SNR> • Channel sensing is possible • Feedback ACK is perfect M Source Terminals Relay hld hil Destination (d) hid Objective: Exploit the capabilities of the relay

7. Cooperation Method 1 • Each terminal transmits HOL packet in its assigned slot (if empty, slot is free) • If D receives successfully, it sends ACK (heard by both the relay and the user) • If D does not succeed but R does: at first sensed empty slot R transmits to D the failed packet • If neither D nor R succeed, packet gets retransmitted by the terminal in next frame • Relay does not keep packets after the end of the frame Idle slots are utilized! Stable throughput for the M terminals Remarks: • Relay has always a finite queue (M packets Max) • Individual terminals interact • Successful service of a packet in a frame depends on whether the other terminals are idle or not

8. Cooperation Method 2 • Each terminal transmits HOL packet in its assigned slot (if empty, slot is free) • If D receives successfully, it sends ACK (heard by both the relay and the user) • If D does not succeed but R does: at first sensed empty slot R transmits to D the failed packet • If neither D nor R succeed, packet gets retransmitted by the relay at next opportunity • Relay keeps all packets it receives correctly Remarks: Again: Idle slots are utilized! Stable throughput for the M terminals and the Relay • Relay has a possibly growing queue • Individual terminals do not interact • They release the unsuccessful packets to the relay • Enhanced version: Relay retransmits only packets of terminals with inferior channels

9. Relationship to Other Schemes • Plain TDMA (no relay help) • Note that at saturation both schemes reduce to TDMA (no idle slots) • But in 2nd method with losses (what does throughput mean?) • Random Access (no relay help) • Selective Decode-and-Forward (interpreted at Network Level) • Relay forwards if it decodes correctly (in next slot) • Must keep “apples and apples”-hence no saturation • Idle slots not utilized • Gets two chances at twice the rate against a simple chance at the lower rate (per fixed packet) • Others in similar vein

10. Results for 2-users 2 R1(S1) 2f2d+21(1-f1d)f1lfld 2f2d R2(S1) 1 1f1d 1f1d+21(1-f2d)f2lfld Method 1 at a specific resource sharing vector (1,2) Comparison

11. Coop-DF: Relay transmits at twice the rate and utilizes one time slots. (Rate and SNR-threshold are related through the Gaussian mutual information formula Coop-DF: Relay transmits at the same rate and utilizes two time slots.

12. Delay • Notoriously difficult for interacting queues • Symmetric System: 2-users

13. Questions • Other possible uses of the Relay • Fundamental Relationship of Information-theoretic view of cooperation to Network-level view • More complex networks possibly tractable (max throughput result and methods can be used)

14. 2nd Example-Cooperation at the Routing Level • Detection of target signal • Objective: maximize PD=prob. of correct detection • Determine routes (not a priori fixed) • Need mapping of PD on link metrics • Sensors cooperate as follows • Every node receives a sufficient statistic from “upstream” • It makes its own measurement as well • Transmits its best sufficient statistic downstream

15. Tandem Case Fusion center • Markovian signal in space (good physical model) • Detection performance is well approximated by sum of terms along the links (one for each link) • Each link’s terms is monotonically related to its length (assume polynomial attenuation and independent noises) • The longer the link the better (the less correlation the better) • Breakthrough of costs, … except… Target X

16. Use in “Blind Routing” • First of all who starts? • Chasing farthest nodes • No guaranteed convergence • Poor performance (correlation along path is not monotonic anymore) Target X Fusion center

17. Possible “Fixes” • Add energy component to metric (moderate the bias toward longer links) • Add exclusion region around visited nodes to enforce directivity • Repeat analysis in 2-dimensions • Remark: • At the heart of the calculation there is an interesting coupling of mutual information and detection performance

18. Summary • Two examples of “Network-level” cooperation • Stable Throughput Region: Fundamental • Are the differences from the Information Theoretic approach leading to interesting new views of cooperation?