Improving Timeliness-Fidelity Tradeoff in Wireless Sensor Networks: Waiting for All and Waiting for Partial Sensor Nodes

Emerging Internet of Things applications pursue both data timeliness and fidelity at the fusion center (FC), raising challenges for network design. This work investigates the optimal node number achieving the best timeliness-fidelity tradeoff. Specifically, we consider a wireless network where homogeneous sensors observe one source simultaneously and deliver their observations to the FC over orthogonal block fading channels. Two scenarios are considered: The FC waits for observations from all nodes and the FC waits for observations from partial nodes. We evaluate the data timeliness and fidelity using the age of information (AoI) and the mean squared error (MSE), respectively. We first present a tight approximation of the average AoI in closed-form and derive a tight lower bound on the MSE of the sensing system. Then, sub-optimal numbers of sensor nodes minimizing a weighted-sum of the average AoI and the MSE are obtained in closed-forms for both scenarios based on high signal-to-noise ratio regime analysis. Iteration algorithms are further provided to approach the optimums. It is shown that the optimal partial number of nodes is proportional to the square root of total number of nodes asymptotically. Numerical results validate the accuracy and effectiveness of the solutions in improving the timeliness-fidelity tradeoff.