Investigation of the impact of compressive sensing on the energy dissipation and lifetime of wireless sensor networks

Wireless Sensor Networks (WSN) are used in many applications by the measurement of physical phenomena in order to monitoring the environment and the status of many civil and military applications. WSN consist a number of energy-limited measuring sensor nodes and at least one base station. Improving the lifetime of WSN is directly related with the energy efficiency of computation and communication operations in the sensor nodes. The Compressive Sensing (CS) theory suggests a new way of sensing the signal through linear measurements possibly needing much less number of measurements compared to the conventional cases if the underlying signal is sparse. This result definitely has implications on WSN energy efficiency and prolonging network lifetime. In this study the effects of acquiring, processing, and communicating CS based measurements on WSN lifetime are analyzed in comparison to conventional approaches. Firstly, some of the iterative signal recovery algorithms alternative for solving the CS problem are investigated and performances on each other based on true reconstruction rates are examined. Then, energy dissipation models for both CS and conventional approaches are built and used to construct a Mixed Integer Programming (MIP) framework that jointly captures the energy costs for computation and communication operations. Numerical analyses are performed by systematically sampling the parameter space (i.e., sparsity levels, network radius, and number of nodes). Our results show that CS prolongs network lifetime for sparse enough signals and is more advantageous for smaller network radii.