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

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

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

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

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

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

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

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

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

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

Computing in Two-Node Network Protocol : Matrix Representation A/B 1 2 3 4 1 2 3 4 0 0 0 1 0 0 0 0 0 1 1 1 11

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Thank you! 26