Dr. Sudharman K. Jayaweera and Amila Kariyapperuma ECE Department University of New Mexico Ankur Sharma Department of ECE Indian Institute of Technology, Roorkee 5 th July,2007 Expand Your Engineering Skills (EYES), Summer Internship Program, 2007

Introduction  Wireless Sensor Networks (WSN) consist of nodes for sensing Temperature Pressure Light Magnetometer Infrared Audio/Video etc  Ad hoc WSN may require inter-sensor communication.

Problem  Nodes are of small physical dimensions Battery operated  Major concern is energy consumption  Failure of nodes due to energy depletion can lead to Partition of sensor network Loss of critical information  Requirement of application/system is that every node should know the data of each other node.

Related Work  Energy aware routing & efficient information processing. [Shah and Rabaey, 2002]  Local compression & probabilistic estimation schemes. [ Luo,2005]  Distributed compression & adaptive signal processing in sensor networks with a fusion center. [ Chou, 2003]

Our Approach i bit

Proposed Algorithm  Sensor j predicts its own reading, depending upon its past readings and readings from other sensors.  Depending upon error between predicted value and actual value i.e. sensor j calculates the compressed bits i using Chebyshev’s inequality method Exact error method

Code Construction  A codebook to encode data X to i bits.  One underlying codebook that is NOT changed among the sensors.  Supports multiple compression rates.

A Tree-based Codebook

Chebyshev’s Inequality Method  To prevent decoding errors with i bits  Chebyshev bound for probability of decoding error  Required value of Value of i :

Exact Error Method  To prevent decoding errors using i bits  As we know exact error in the prediction of sensor data X, number of bits are  Send extra bits also, specifying the number of bits in the message.

Encoder Sensors  X is stored as the closest representation from 2 n values in the root codebook (A/D converter).  Mapping from X to the bits that specify the subcode-book at level i is done using

Decoder Sensors  Decoders receive i -bit value & code sequence f(x).  Traverse the tree starting from LSB of code sequence to find appropriate subcode book, S.  Calculates the side information Y as  Decodes the side information Y, to the closest value in S as

Correlation Tracking  Linear prediction method Analytically tractable Optimal when readings can be modeled as i.i.d. Gaussian random variables.  First sensor always sends its data compressed w.r.t. its own past data.  Prediction of X is where

Least-Squares Parameter Estimation  Prediction error is  Choose filter coefficients in order to minimize weighted least squares error.  Least squares filter coefficient vector at time k is given by where

Recursive Least-Squares (RLS) Algorithm  Filter coefficient computation is performed adaptively using RLS where and  For initialization, each sensor sends uncoded data samples.  In our approach reference sensor updates the corresponding coefficients and sends them to all other sensors.

Decoding Errors  No decoding errors in exact error method.  In Chebyshev’s method, no of encoding bits are specified within a given probability of error and after every 100 samples.  Leads to few decoding errors, but results in higher compression.

Implementation & Performance  Simulations were performed for measurements on humidity data.  We assumed a 12 bit A/D converter with a dynamic range of [-128,128].  Simulated results for about 18,000 samples for each sensor (total of 90,000)  Sensor orderings are randomized every 500 samples.  For RLS training, first 25 samples of each sensor are transmitted without any compression.  Coefficients are updated and shared after every 500 samples.

Exact Error implementation  With each code sequence, extra 4 bits to specify the number of bits are also sent.  Decoding Error = 0  Average Energy Saving %= 43.34%

Tolerable Noise vs. Prediction Noise

Chebyshev’s Inequality method  Encoding bits are specified every 100 samples  Case I: Probability of Error ( P e ) = 0.5%  Average Decoding Error % = 0.07%  Average Energy Saving % = 45.74%

Tolerable Noise vs. Prediction Noise

Chebyshev’s Inequality method  Case II: Probability of Error ( P e ) = 1.0%  Average Decoding Error % = 0.13%  Average Energy Saving % = 49.74%

Chebyshev’s Inequality method  Case II: Probability of Error ( P e ) = 1.5%  Average Decoding Error % = 2.29%  Average Energy Saving % = 52.27%

Comparison Exact Error MethodChebyshev’s Method  ZERO probability of decoding error  Compression is low (due to extra bit information)  Strict bound  ‘Instantaneous approach’  Probability of decoding error within a required bound.  Higher Compression can be achieved by varying required probability of error.  Loose bound  ‘Average approach’.

Probability of Error vs. Energy Savings

For Temperature Data  Exact error method Average energy savings % = 56.66% Average decoding error % = 0  Chebyshev’s method ( P e = 0.01 ) Average energy savings % = 66.98% Average decoding error % = 0.61%

For Light Data  Exact error method Average energy savings % = 33.52% Average decoding error % = 0  Chebyshev’s method ( P e = 0.01 ) Average energy savings % = 19.29% Average decoding error % = 1.13%

Conclusions  Energy savings achieved through our simulations are conservative estimates of what can be achieved in practice.  Further work can be done on Better predictive models. Better probability of error bound.  Can be integrated with an energy saving-routing algorithm to increase the energy savings.

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