Age of Correct Sensing in Sensing-and-Then-Transmit ISAC Networks

This paper investigates the sensing-and-then-transmit (SAT) integrated sensing and communication (ISAC) network, where a multi-functional base station (MBS) senses the target's state and then transmits the sensed results to the receiving node (RN). To measure the timeliness of the SAT process, we define a novel metric called Age of Correct Sensing (AoCS). To enhance the system's AoCS, we propose a pipelined SAT ISAC (P-SAT ISAC) paradigm, where the MBS simultaneously transmits individual beams to perform sensing and communication. We derive the mathematical expression of the probability of detection (PD), the probability of false alarm (PFA), and the probability of communication outage (PCO), based on which, the AoCS of the P-SAT ISAC is quantified. Furthermore, we formulate an expected AoCS minimization problem by optimizing the power splitting factor for sensing and communication to explore the achievable lower bound of AoCS. Then, the minimum expected AoCS is found by developing a linear search based algorithm. Simulation results validate the theoretical analysis on PD, PFA, and PCO, and also show the impact of system parameters on them, as well as the minimum achievable expected AoCS. Compared with the existing alternating SAT ISAC (A-SAT ISAC), our proposed P-SAT ISAC achieves an average reduction in expected AoCS of 38.97%, demonstrating the efficiency of the proposed pipelined sensing and communication paradigm in improving system timeliness.