Signal Processing & Communication for Smart Dust Networks

Haralabos (Babis) Papadopoulos

ECE Department

Institute for Systems Research

University of Maryland, College Park

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

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:

Multiple Access ProtocolsMotivation• 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

FDMATDMA/FDMA

Frequency

time

Signal

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

TDMA-FDMA Channel Reuse in Ad-hoc Network

T1 T2 T3 T4

F1 N1 N6

F2 N2

F3 N3 N5

F4 N4

T1 T2 T3 T4

F1 N1 N1

N6

F2 N2N2

F3 N3 N5

F4 N4

Slot Assignment

Protocols for nodes N1, N2

Ad-hoc Network

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)

Example: Computation of Global MaximumObjective: 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

Computation of Weighted AveragesRemark

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

1st-Order Fusion Rules

o Locally constructed fusion rule (using reciprocity and balancing)

o z=<x> 1 is eigenvector of W=I+ with eigenvalue 1o proper choice of convergence of each node state to global average with increasing n

jijiii

jiji ji

,,

, ,

not if 0 connected; are , nodes if 1 :matrixty connectivi

parameterdiffusion

sensorth at t measuremen ]0[ :tionInitializa

) (h wit]1[ ][ :form)(matrix ly,Collective

ixz

IWnWn

ii

zz

Convergence of 1st-Order Fusion RulesPerformance metric:

RMSE depends on choice of parameter

0 at time MSE node aggregate

at time MSE node aggregate ][RMSE : at timeerror -square-mean Relative

nnn

iii

iii

iii

iii

,2,

,

1

,

max

:solid

max

1 :dot-dash

optimal asympt. :dashed

Improved Higher-Order Fusion Rules

convergence-mode histograms

top-left: 1st-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

parameter shaping ,1

1)(

:filter shaping igenvalue

2

c

czzH

e

RMSE of Filtered RulesRelative MSE vs. number of iterations

6.0 ,3.0 ,0 and , with rules filtered :curves solidlower ly successive

with ruleorder -1 :dot-dash

with ruleorder -1 :dashed

1

maxst

st

c

RMSE Improvements due to Filteringfiltering 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 1st order rule over number of iterations needed by associated filtered rule to achieve target RMSE (20dB-60dB)

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

Related PublicationsD. 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.