1. Computing and Compressive Sensing in Wireless Sensor Networks
Zhenzhi Qian, Chu Wang
Department of Electronic Engineering
Shanghai Jiao Tong University, China 1

2. Outline Introduction Definition & Model Computing in Two-Node Network
Function Computation Rate
Compressive Sensing : A Basic Application
Future Work 2 2

3. Introduction Wireless Sensor Networks Task of sensing the environment
Task of communicating function values to the sink node
Function Types
Type-sensitive
e.g. Network of temperature sensors
Type-threshold
e.g. Alarm network
Aggregate functions under end-to-end flow
Energy-constrain
Memory-constrain
Bandwidth-constrain 3

4. Introduction An alternative solution In-network computation
Perform operations on received data
A series of Fundament al Issues in In-Network Computation
How best to perform distributed computation
What is the optimal strategy to compute
Challenges in WSNs Data Gathering
Global communication cost reduction
Energy consumption load balancing 4

5. Outline Introduction Definition & Model Computing in Two-Node Network
Function Computation Rate
Compressive Sensing: A Basic Application
Future Work 5 5

6. Definition & Model is the set of the measurement data
is the function used for computation
is the Euclidean distance between sensor i and sensor j
is the sensor’s transmission range
Collocated Network(figure.(a))
The network with ,for all
Random Planar Network
The nodes and the sink node is i.i.d distributed, and is chosen to ensure connectivity by multi-hop communication 6

7. Outline Introduction Definition & Model Computing in Two-Node Network
Function Computation Rate
Compressive Sensing: A Basic Application
Conclusion & Future Work 7 7

8. Computing in Two-Node Network
The two connecteed processors can exchange bits one at a time over the link
When A and B both know the function value ,the communication terminates
This problem is minimizing computation time given a throughput constrained link between processors and an input split between processors A B 8

9. A B Computing in Two-Node Network A general protocol functionality
Decide which node to transmit
Input : previously transmitted nodes
Decide the value of the bit to be transmitted
Input : input value + previous transmission
A naïve protocol
The communication complexity of function is
slots
Optimization ? Lower bound ? A B 9

10. A Computing in Two-Node Network
The Lower bound of communication complexity:
Any two distinct function values must correspond to different sequences of transmitted bits A 10

11. Computing in Two-Node Network
Protocol : Matrix Representation
A/B 1 2 3 4 11

12. Computing in Two-Node Network
There are several ways to derive the lower bound of the number of the partitions required
Rank-based:
-based:
Prove : 1) ONE ROUND RANK (AT MOST) ½
2) similar to the above 12

13. Outline Introduction Definition & Model Computing in Two-Node Network
Function Computation Rate
Compressive Sensing : A Basic Application
Conclusion & Future Work 13 13

14. A tree rooted at the collector node
Function Computing Rate
Scenario of Sensor network Computation
A tree rooted at the collector node 14

15. Function Computing Rate
Function types and corresponding results:[kumar]
Histogram: statistic of node measurements
Computational rate: 15

16. Function Computing Rate
Function types and corresponding results:
Type-sensitive:
A symmetric function is defined as type-sensitive if exists some and integer N, such that for all
and any , there are two subsets of , satisfy that:
A easy note :
Any input of the sensor network changes, the sensitive function value changes due to the local small difference.
Computing rate:
In a collocated network:
Examples of type-sensitive functions:
Average,median,majority,histogram
Computing rate:
In a random planar multihop network: 16

17. Function Computing Rate
A example to help understand threshold function
Function types and corresponding results:
Type-threshold:
A symmetric function is defined as type-threshold if exists a nonnegative -vector , called the threshold vector , so that
for all
A easy note:
Suppose a protocol of advancing the threshold:
When a given sensor measurement is above the threshold, it is considered by the computation, otherwise it can be safely ignored
Node : Tall,wealthy,handsome
Node: the opposite
The function : white wealth pulchritude
Thresholds 17

18. Function Computing Rate
Examples of type-threshold functions:
Maximum, minimum, k-th largest value
Computing rate in collocated network:
Computing rate in random planar multi-hop network: 18

19. Outline Introduction Definition & Model Computing in Two-Node Network
Function Computation Rate
Compressive Sensing : A Basic Application
Conclusion & Future Work 19 19

20. Compressive sensing Introduction of compressive sensing[2009 mobicom]
Baseline data collection
Compressive data gathering 20

21. Compressive sensing Analysis : The sink obtains M weighted sums ,
Where represents the i-th sum round’s corresponding j-th sensor nodes coefficient. This coefficient is random a value. But it can be achieved at the sink node by preserving the series of pseudo random numbers of each sensor .Meaning the matrix is saved beforehand.
N total nodes and M rounds of gathering exists. 21

22. Compressive sensing Data recovery
Find a particular domain ,and sensor readings
is a K-sparse signal in it , thus are the coefficients, which given as:
The domain is chosen by yourself. Usually the DCT and wavelet is preferred.
The compressive sampling theory have:M should satisfy
if the K-sparse signal is resconstructable. 22

23. Compressive sensing Data recovery
We thus summary the conditions for now:
M sums at the sink node with efficient amount for reconstruction by the restraints given previously.
where and are known to us.
As is given in the compressive sensing theory, the problem is converted to a l1-norm minimization version :
Find satisfying
where
This can be solved by a linear programming tech[13]. And finally using we can obtain the sensor readings. 23

24. Outline Introduction Definition & Model Computing in Two-Node Network
Function Computation Rate
Compressive Sensing: A Basic Application
Future Work

25. Future Work Consider mobility in the WSNs Gossip algorithm
Coding strategy:LDPC

26. Thank you! 26