1. Active Wireless Sensing in Time, Frequency and Space Akbar M. Sayeed (joint work with Thiagarajan Sivanadyan) Wireless Communications Research Laboratory Electrical and Computer Engineering University of Wisconsin-Madison http://dune.ece.wisc.edu Supported by NSF IPAM 2007 Mathematical Challenges and Opportunities in Sensor Networks

2. Motivation Physical spatial signal field Sensor network: spatio-temporal sampling In-network processing  Information processing in sensor networks  Sensors communicate and relay information among themselves Disadvantages  Excess delay: Multiple multihop transmissions across the network  Excess energy consumption: Additional tasks such as routing and coordination among nodes E.g: Consensus algorithms require radio transmissions (Dimakis et al. IPSN ‘06)

3. Wireless Information Retriever (WIR) Downlink: Space-time interrogation waveforms (high power) Uplink: Weak sensor response (energy-limited) Active Wireless Sensing Alternative Approach for Rapid Information Retrieval Consensus achieved in two channel uses

4. Other Motivations and Connections  Network to fusion-center communication architecture  Advances in RF technology – reconfigurable RF front-ends –Source-channel matching - Information retrieval at multiple spatial resolutions –New tradeoffs between rate, energy and reliability/fidelity  Connections –Imaging sensor networks (Madhow) – radar –Multipath channels, multi-antenna (MIMO) communication –Joint source-channel communication (Gastpar & Vetterli) Distributed beamforming (Mudumbai et.al. 2005) –Distributed time-reversal (Barton et.al. 2005) –Cooperative/opportunistic relaying (Scaglione) –Cognitive radio/radar

5. Overview  Salient characteristics –“ Dumb ” sensors: limited computational power, relatively sophisticated RF front-ends –“ Smart ” Wireless Information Retriever (WIR): computationally powerful, equipped with an antenna array  Basic protocol (Line-of-sight communication) –WIR interrogates sensor ensemble with wideband space – time waveforms –Sensors respond to WIR interrogation signals –WIR exploits the space-time characteristics of sensor ensemble response for information retrieval  Interplay between sensing, processing, and communication –Canonical sensing configurations : spatial scale of signal correlation and/or network cooperation –Matched source-channel communication: energy efficiency and sensing capacity  AWS over multipath channels

6. Basic Communication Protocol WIR Sensor 1 Sensor 2 carrier tone s(t) Sensor 1 receives s(t) Sensor 2 receives s(t) Carrier synch: The WIR transmits a carrier tone to synchronize the frequency of local sensor oscillators Interrogation: The WIR transmits a wideband spatio-temporal waveform s(t) - Temporal pseudo noise (PN) code Temporal code acquisition by sensors Sensor transmissions: sensors modulate the PN code to transmit their (compressed) measurements to the WIR: - Non-coherent transmission - Coherent transmission (sensor phases stable over two channel uses) t t t Fixed Delay T

7. Line-of-Sight Sensing Channel K : number of sensors or active scatterers PN code : q(t) Duration : T Bandwidth : W M-element array (ULA) at the WIR : sensor data : sensor phase : sensor delay : sensor angle Array response vector Received signal

8. Sensor Resolution in Angle-Delay  Delay resolution: resolve the signals in each spatial beam by correlating with uniformly delayed versions of the PN code Delay A single sensor in each resolution bin for large W Angle  Spatial resolution: resolve the received signals from M fixed uniformly-spaced directions via receive beamforming Angle Delay

9. Sufficient Statistics: Angle-Delay Matched Filtering Uniform Angle-Delay Sampling

10. Angle-Delay Matched Filtering

11. Sensor Angle-Delay Signatures Angle-delay Channel Coefficients Sensor Angle-Delay Signature

12. Sensor Localization For sufficiently large W, only one sensor in any angle-delay bin

13. System Equation – Max Resolution – Angle-delay signature vector of i-th sensor – Angle-delay matched filter outputs – Sensor transmission energy

14. Ideal Scenario: Orthogonal Signatures Sensor locations Delay Angle Angle Delay Sampling Orthogonal  No interference between sensor transmissions Sensor signature

15. Reality: Inter Sensor Interference Sensor locations Delay Angle Angle Delay Sampling Non-orthogonal  inter sensor interference Sensor signature

16. Space-Time Dimensions in AWS TW temporal dimensions (length of spreading code) M spatial bins L < TW delay bins angle-delay resolution bins parallel (interfering) channels between the sensor ensemble and the WIR

17. Canonical Sensing Configurations # Independent bits per channel use # Sensors transmitting each bit N = K = 108 M=9, L=12

18. Partitioning of Sensor Transmissions and MF Outputs Effective angle-delay signature associated with the bit in i-th group

19. Information Retrieval at Max Resolution Simplest receiver structure for recovering bit from i-th group Match filtering to angle-delay signature

20. MMSE Interference Reception Interference suppression Signature-matched filtering

21. BER Performance Int. Supp: No error floors SNR loss More bits per channel use Matched Filter: Error floors bits per channel use Per sensor(dB)

22. Source-Channel Matching What if we could map the identical transmissions from sensors in each group coherently into one angle-delay bin at the WIR? Sensor transmissions Reception at the WIR in angle-delay bins Max. resolutionSource-channel matching L=12 M=9 Dimension reduction by

23. System Equation: Source-Channel Matching Effective “focussed” angle-delay signatures Coherent angle-delay “focussing” (coherent MAC) (max resolution)

24. Max-Resolution Versus Matched Source- Channel Communication versus

25. How do we do Source-Channel Matching? Highest resolutionSource-channel matching Array reconfiguration Distributed time-reversal to line up sensor delays in each group Distributed beamforming in each group

26. Alternative Approach Decreasing antenna spacing  decreasing carrier frequency Alternative to time-reversal: decreasing signaling bandwidth Distributed beamforming in each low-resolution bin

27. Sensing Capacity Fraction of temporal dimensions used Angle-delay Parallel channels Received SINR per parallel channel Ideal case: SINR  SNR bps/Hz

28. Capacity: Max Resolution (Ideal) Maximum parallel channels Minimum SNR per parallel channel Minimum parallel channels Maximum SNR per parallel channel Sensing capacity increases monotonically with Coherence gain Array gain

29. Capacity: Source-Channel Matching Multiplexing gain versus received-SNR tradeoff Coherent “beamforming” in each group/parallel channel Each parallel channel is a coherent MAC (AS & Raghavan 2006) Capacity-maximizing configuration

30. Sensing Capacity Comparison: With or Without Source-Channel Matching SNR Max. resolutionSource-channel matching (adaptive resolution)

31. AWS over Multipath WIR Sensor Ensemble Scatterer LOS Path Scattered Path

32. AWS over Multipath: Multiple Bounce WIR Sensor Ensemble Scatterer LOS Path Scattered Path

33. System Equation LOS: Scatterer Signature Matrix (full rank) Ensemble- To-Scatterer Coupling Matrix (full rank) Ensemble Signature Matrix (low rank) Multipath: Effective signature of i-th sensor: Average received per-sensor SNR:

34. Impact of Multipath Pros: Higher capture of transmitted sensor energy Higher spatio-temporal diversity Distinct sensor signatures for denser ensembles Distinct sensor signatures with smaller arrays and bandwidths Signal dispersion in space and time Cons: Sensor localization information lost Fading

35. Sensor Signatures – Line-of-Sight (LOS) Paths K = 108 sensors in 3 angle – 4 delay bins

36. Scatterer Signatures Scatterer Positions 27 Scatterers Signatures Induced by a Single Sensor: Single Bounce Scattering 108 Scatterers Signatures Induced by a Single Sensor: Multiple Bounce Scattering

37. Dimensions Induced by Sensor Ensemble Scatterer Positions 27 Scatterers Single Bounce Scattering 108 Scatterers Multiple Bounce Scattering (Angle=9, Delay = 38) Dims = 142 Dims = 228 (Angle=9, Delay = 46) (Angle=9, Delay = 18) Dims = 102 (Angle=9, Delay = 24) Dims = 118

38. Effective Sensor Signatures Single Bounce Scattering Multiple Bounce Scattering

39. Eigenvalues of the Coupling Matrix Sum of Eigen Values: LOS - 42.12 27 Scat. – 2982 ; 54 Scat. - 5944 108 Scat. – 11590 ; 162 Scat. - 17587 Multiple Bounce Scattering Single Bounce Scattering Sum of Eigen Values: LOS - 42.12 27 Scat. – 2651 ; 54 Scat. – 5307 108 Scat. – 10318 ; 162 Scat. – 15704

40. Conclusions and Challenges  Flexible architecture for information retrieval in sensor networks –Complementary to in-network processing (latency, energy efficiency) –Reconfigurable wideband multi-antenna RF front ends –X-fertilization between space-time wireless communications, radar, and sensor networks –Cognitive wireless communications and sensing  Distributed source-channel matching –Multi-resolution space-time sensing and communication –New tradeoffs involving energy, information rate, fidelity  Challenges and future research –AWS over multipath – sensor addressing via space-time reversal –Interplay with in-network processing –Optimization for inference applications –Learning unknown signal fields and channels