Rethinking the performance of isac system: from efficiency and utility perspectives

Integrated sensing and communications (ISAC) is an essential technology for the 6G communication system, which enables the conventional wireless communication network capable of sensing targets around. The shared use of pilots is a promising strategy to achieve ISAC. It brings a trade-off between communication and sensing, which is still unclear under the imperfect channel estimation condition. To provide some insights, the trade-off between ergodic capacity with imperfect channel estimation and ergodic Cramer-Rao bound (CRB) of range sensing is investigated. Firstly, the closed-form expressions of ergodic capacity and ergodic range CRB are derived, which are associated with the number of pilots. Secondly, two novel metrics named efficiency and utility are firstly proposed to evaluate the joint performance of capacity and range sensing error. Specifically, efficiency is used to evaluate the achievable capacity per unit of the sensing error, and utility is designed to evaluate the utilization degree of ISAC. Moreover, an algorithm of pilot length optimization is designed to achieve the best efficiency. Finally, simulation results are given to verify the accuracy of analytical results, and provide some insights on designing the slot structure.