Age of Aggregated Information: Timely Status Update with Over-the-Air Computation

Fast wireless data aggregation is a critical design challenge in Internet-of-Things (IoT) networks. In this paper, we consider a real-time status update IoT network, where an access point (AP) aims to aggregate data from multiple IoT devices using over-the-air computation (AirComp). To evaluate the freshness of the aggregated data at the AP, we propose the metric of age of aggregated information (AoAI), extended from the age of information (AoI), which is defined as the time elapsed since the generation of the latest valid aggregated data received at the AP. An aggregated status update is considered to be valid if the AirComp distortion, quantified by the mean-squared-error (MSE), is smaller than a pre-determined threshold. We formulate a constrained Markov decision process (MDP) problem for minimizing the average AoAI subject to the average transmit power constraint of each IoT device. The formulated constrained MDP problem is then reformulated as an unconstrained MDP problem by using the Lagrangian approach. By analyzing the structure of the MDP, we propose a state aggregation procedure to reduce the computational complexity. We further propose both offline and online scheduling algorithms to solve the problem. Simulation results show that the proposed algorithms significantly outperform the baseline algorithm with a fixed scheduling threshold in terms of the AoAI, and also strike a good balance between the AoAI and the total power consumption.