1. Signal Processing & Communication for Smart Dust Networks Haralabos (Babis) Papadopoulos ECE Department Institute for Systems Research University of Maryland, College Park

2. Signal Processing & Communication Objectives Desired tasks algorithms for data processing, communication, and fusion compute statistics of measurements over large wireless networks maximum, average, locally-averaged (in space) signal estimates Algorithmic Properties  energy-efficient  large networks with changing topology  locally constructed  fusion objective  exploit compression benefits via distributed fusion  scalable  fault-tolerant

3. Point-to-Point Wireless Communication Transmitter: source-coding: quantization + compression  information bits channel coding: Hagenauer’s rate-compatible punctured convolutional codes controlled redundancy in order to achieve target bit-error-rates over channel unequal-error protection frequency-shift-keying (FSK) modulation good tradeoffs in performance vs. complexity/robustness of implementation Receiver:

4. Multiple Access Protocols Motivation abundant bandwidth  nodes are multiplexed in frequency (suff. spaced to avoid interference) RF circuitry limitations: each node can broadcast continuously but receive only at only one channel at any given time  also need multiplexing in time to receive data from multiple nodes during a single frame TDMA-FDMA protocol ( multiplexing in both time and frequency) each node has unique time-frequency slot for transmission during any time slot, each node can receive at most at one frequency slot Time Signal TDMA Frequency FDMA TDMA/FDMA Frequency time Signal

5. Ad-hoc Networking Setting two-way local communication between closely located (“connected”) sensor nodes each sensor node receives messages sent by connected nodes each sensor broadcasts messages to connected nodes Advantages fault tolerant, readily scalable space-uniform resource usage transmit power efficient Issues need for networking

6. TDMA-FDMA Channel Reuse in Ad-hoc Network T1T2T3T4 F1N1N6 F2N2 F3N3 N5 F4N4 T1T2T3T4 F1N1 N6 F2N2 F3N3 N5 F4N4 Slot Assignment Protocols for nodes N1, N2 Ad-hoc Network

7. Ad hoc Networks for Fusion Related work conventional ad-hoc networks, amorphous computing (Sussman, MIT) Distinct features of fusion problem interested in underlying signal in data (e.g, target location, average or highest temperature), not all data info about signal “spread” over many nodes multiple destinations Remarks advantages: data compression in fusion, inherent scalability key problem: communication loops (contamination of information)

8. Example: Computation of Global Maximum Objective: " compute maximum measurement (e.g., compute highest sensed temperature) Approach: " sequence of local maxima computations Resulting dynamics: " each node state converges to global maximum (highest temperature) in finite number of steps provided network is connected

9. Computation of Weighted Averages Remark not all local averaging fusion rules yield global average (data contamination) Approach locally constructed fusion rules [Scherber & Papadopoulos] that asymptotically compute weighted averages of functions of individual measurements distributed, fault-tolerant, readily scalable Example: 200 nodes in a circle randomly placed probabilistic model for connectivity function of node distance

10. 1 st -Order Fusion Rules o Locally constructed fusion rule (using reciprocity and balancing) o z= 1 is eigenvector of W=I+  with eigenvalue 1 o proper choice of   convergence of each node state to global average with increasing n

11. Convergence of 1 st -Order Fusion Rules Performance metric: RMSE depends on choice of parameter 

12. Improved Higher-Order Fusion Rules convergence-mode histograms top-left: 1 st -order rule top-right: filtered rule with c=0.1 bottom-left: filtered rule with c=0.3 bottom-right: filtered rule with c=0.6

13. RMSE of Filtered Rules Relative MSE vs. number of iterations

14. RMSE Improvements due to Filtering filtering yields savings in # of iterations needed to reach a target RMSE level computation savings metric: iteration gain factor: ratio of number of iterations needed by 1 st order rule over number of iterations needed by associated filtered rule to achieve target RMSE (20dB-60dB)

15. Properties of Local Rules for Computing Averages & Applications Properties inherently distributed, locally constructed, fault tolerant, readily scalable have been extended to perform computations with non-contributing nodes Applications weighted averages of functions of measurements global & localized averages, variances, power, geometric means chemical- & bio-hazard monitoring and detection localized monitoring, threshold detection based on majority voting surveillance: target detection and classification target localization target tracking any computations that can be decomposed into computing weighted averages of local functions of measurements

16. Related Publications D. S. Scherber and H. C. Papadopoulos, “Distributed computation of averages over ad-hoc networks,” submitted to IEEE J. Select. Areas Commun., Dec. 2003. D. S. Scherber and H. C. Papadopoulos, “Locally constructed algorithms for distributed computations in ad-hoc networks,” submitted to Inform. Proc. Sensor Net. Conf., 2004. T. Pham, B. M. Sadler, and H. C. Papadopoulos, “Energy-based source localization via ad- hoc acoustic sensor networks,” in 2003 IEEE Workshop on Statist. Signal Proc., Sep. 2003. H. C. Papadopoulos, G. W. Wornell and A. V. Oppenheim, “Sequential signal encoding from noisy measurements using quantizers with dynamic bias control,” IEEE Trans. Inform. Theory, vol. 47, no. 3, pp. 978-1002, Mar. 2001. M. M. Abdallah and H. C. Papadopoulos, “Sequential signal encoding and estimation for distributed sensor networks,” in Proc. IEEE Int. Conf. Acoust. Speech, Signal Proc., pp. 2577-2580, May 2001.