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Distributed Wavelet Transform for Wireless Sensor Networks: TinyOS Implementation

Author: J. Ryan Stinnett ( DSP Group, Rice University


This project implements data compression for wireless sensor networks (WSNs) by using a distributed wavelet transform. This compression system lowers the number of devices which need to transmit data to a base station, and thus reduces power consumption and increases the average lifetime of the network.


Code running on the WSN devices, or "motes", was written in nesC for TinyOS and tested on Crossbow's MicaZ platform. Before working on the transform itself, I created several components that provide essential system services. The first of these was a suite of networking components. As the focus of this project is not on routing protocols, I opted for simplicity by using basic broadcast and unicast protocols. The broadcast protocol waits for packets with a sequence number larger than the last sequence number received, and then repeats those new packets a set number of times. The unicast protocol uses a static routing table to determine the next hop for a given packet.

Above these protocols, I built a multi-packet fragmentation and reassembly service. It allows for bidirectional communication of any data size. TinyOS 1.x uses a fixed data length of 29 bytes, so expanding beyond this limit in a reusable manner simplifies code significantly. By using small descriptor records, this system can even rebuild data structures that use pointers or variable-length arrays. These techniques were used to send the initial wavelet transform parameters to the motes and also to request statistical data from the motes about network traffic.

The distributed wavelet transform[1] is the core application running on top of these and other standard TinyOS system services. Currently only a spatial transform across the mote network has been implemented, but a transform in the time domain will be added soon. To ensure that each mote runs each scale of the transform at the same time, a finite state machine with fixed-length delays between each state is used. The scheme assumes clock synchronization between motes. A clock synchronization protocol specific to WSNs has already been proposed.[2]

To achieve data compression, each mote compares its value against a list of target values from the sink, which are arranged in decreasing order. Each mote compares its results from the current round of the wavelet transform with the target values. The first target value that is less than the result value determines the transmission band. Each mote assigned to a specific band transmits its data back to the sink at roughly the same time. When the sink determines it has received enough values to reconstruct a good approximation of the original data, it broadcasts a stop message to prevent further bands from being transmitted. This message also includes updated target values that will be used during the next transform round.

For the sink node, I created a variety of support tools in both Java and MATLAB. It took several revisions to design a good scheme for mote communication in Java that could support all of the various system tools as well as the wavelet transform itself. With that in place, these tools simply try to provide a logical user interface to the various options and functions of the motes.


Though there are many things I learned while working on this project, what stood out in my mind the entire time was the importance of thoroughly debugging code and including as many tests and checks to ensure proper operation. When writing code that runs purely on modern PCs, it is easy to be sloppy about such things because you can always attach a debugger and resolve the issue. When working with the motes, you can't debug code directly on the motes themselves. Also, they are dependent on messages from other devices, so inspecting the code on one device may not be enough to see the whole issue. Luckily, TinyOS includes TOSSIM, which can simulate an entire mote network on a PC. This tool has helped resolve bugs countless times.

When I started working on the multi-packet transmission system, I quickly discovered that my understanding of pointers in C needed improvement. I found great tutorials online that helped me grasp the relationship between pointers and arrays, without which I doubt I could have gotten the system to work at all. It is this relationship that I exploited to rebuild hierarchical data structures from a simple data stream.

To verify good network operation, we wanted to capture various metrics about the messages that pass through each mote. One of these metrics is the median of the received signal strength. Ordinarily, one would need to store every measurement to find the median, but that is not a practical on these motes with such limited memory. I originally tried to use the mote's flash storage to hold all the values, but that became too complex for such a simple question. Instead, I used a compact technique for estimating the median from only a few values[3], which can remain entirely in memory.

Another issue I encountered was with sensor values that would intermittently be far larger than was even possible for the sensor itself. After looking more closely at documentation, I found that on the MicaZ, one of the sensors shares an interrupt line with the radio. If a packet is received while trying to read this sensor, its value will be corrupted. This issue itself would have been easy enough to work around, but it was compounded by conflicting files in the TinyOS tree I was using, which prevented the correct system files from being used.

Overall, this project has given me extensive, hands-on experience with the difficulties of embedded development. While the problems are often very frustrating at times, there is always a solution to be found if you look hard enough.


  1. R. Wagner, R. Baraniuk, S. Du, D.B. Johnson,
    and A. Cohen. An Architecture for Distributed Wavelet Analysis and Processing in Sensor Networks. In Proceedings of the Fifth international Conference on information Processing in Sensor Networks (Nashville, Tennessee, USA, April 19 - 21, 2006). IPSN '06. ACM Press, New York, NY, 243-250. (pdf | ps)
  2. S. PalChaudhuri, A.K. Saha, and D.B. Johnson. Adaptive Clock Synchronization in Sensor Networks. In Proceedings of the Third international Symposium on information Processing in Sensor Networks (Berkeley, California, USA, April 26 - 27, 2004). IPSN '04. ACM Press, New York, NY, 340-348. (pdf)
  3. R. Jain and I. Chlamtac. The P2 algorithm for dynamic calculation of quantiles and histograms without storing observations. Commun. ACM 28, 10 (Oct. 1985), 1076-1085.

Future Plans

While data compression using the wavelet transform is complete, there are still many features and improvements that could still be added. A summary of the most important of these follows:

  • Time domain transforms for further compression
  • Separate wavelet core from system services for reuse
  • Rework networking systems to save resources and improve compatibility with other routing protocols
  • Support any number of abstract inputs, instead of two fixed sensors
  • Make Java objects easier to call from within MATLAB


I never would have been able to complete this project with the advice and support from Ray Wagner and Dr. Baraniuk, as well as numerous others. Thanks again for all the help!


Distributed Wavelet Transform for Wireless Sensor Networks: TinyOS Implementation





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