Timeliness-Distortion Tradeoff in Wireless Sensor Networks: The Optimal Node Number

Pursuing both data freshness and preciseness in emerging Internet of Things applications brings big challenge for network design. This work investigates the optimal node number achieving the best fidelity-timeliness tradeoff. Specifically, we consider a wireless sensor network where multiple sensors observe one source simultaneously and deliver the observations to Fusion Center (FC) over orthogonal channels. We assume that the FC waits for observations from only partial nodes. We evaluate the fidelity and timeliness using mean squared error (MSE) and age of information (AoI) metric respectively. Firstly, explicit expressions of AoI and MSE are derived. Secondly, a closed-form approximate optimal number of sensor nodes is obtained to achieve the minimum weighted-sum of AoI and MSE. Iteration algorithm is further provided to approach the optimum. It is proved that the optimal number of partial nodes is proportional to the square root of number of total nodes. Numerical results verify that the proposed near-optimal node number is accurate and can significantly improve the fidelity-timeliness performance.