Energy Analysis in Single Cluster WSNs with Power Control and In-network Data Compression
Dajiang Li, Jacek Ilow · 2022
Analytical expressions for the energy associated with data collection in Wireless Sensor Networks (WSNs) is an important tool when operating integrated sensing and transmitting devices constrained by limited battery life-time. This paper develops a new method of finding the energy dissipated by sensors due to (i) variable times associated with the transmission of in-network compressed data and (ii) transmit power adjusted to overcome deterministic attenuation of signals with distance in various radio propagation environments. Specifically, semi-analytic expressions are derived for energy associated with data aggregation and communication when sensor nodes send data to a single cluster head (sink) located at the origin and assuming that sensors are distributed within the cluster according to a two dimensional (2-D) Poisson point process. The compressed representations of the sensed phenomenon at various nodes in the system exploit spatial correlation among sensor measurements and, similarly as transmit powers, are dependent on the distances between nodes and the sink. The starting point for the analysis is the observation that node distances to the sink form a gamma distribution. By using this model, the dissipated energy is derived by finding the fractional moments of the gamma distribution. With sensors distributed randomly in a plane, close agreement is found between the calculated and simulated results for dissipated energies in different propagation and sensing conditions.