Timely Information Delivery in Joint Sensing and Communication Systems With Average Power Constraints

Joint sensing and communication (JSC) systems aim to leverage the same spectral resources for both communication and sensing tasks within a single system. These systems have the potential to enhance sensing capabilities through advanced communication techniques, while also utilizing precise localization and tracking information from sensing technologies to improve communication. However, the integration of information obtained from sensing and transmitted in communication is not yet fully understood. This paper investigates the challenge of guaranteeing timely delivery of sensing information within JSC systems. We introduce a novel metric, termed as the age of estimation information (AoEI), which integrates radar mutual information (MI) and age of information (AoI). This unified metric effectively captures both the passage of time and the accuracy of estimation information, making it well-suited for the JSC system. Further, we delve into the joint optimization of time and power allocation for a single JSC node with both sensing and communication capabilities. Our objective is to minimize the long-term average AoEI while adhering to a long-term average power constraint. To tackle this problem, we formulate it as an average-reward constrained Markov decision process (CMDP) and propose a model-free constrained deep reinforcement learning (CDRL) algorithm, namely the average policy optimization (APO)-Lagrangian based algorithm. Simulation results demonstrate that our proposed algorithm effectively meets the constraint in dynamic and uncertain environments while achieving a favorable balance between AoEI and power consumption. Additionally, our algorithm outperforms four baseline schemes, showcasing its superior performance.