Reference Signal-Based Waveform Design for Integrated Sensing and Communications System

Integrated sensing and communications (ISAC) as one of the key technologies is capable of supporting high-speed communication and high-precision sensing for the upcoming 6G. This paper studies a waveform strategy by designing the orthogonal frequency division multiplexing (OFDM)-based reference signal (RS) for sensing and communication in ISAC system. We derive the closed-form expressions of Cram\'er-Rao Bound (CRB) for the distance and velocity estimations, and obtain the communication rate under the mean square error of channel estimation. Then, a weighted sum CRB minimization problem on the distance and velocity estimations is formulated by considering communication rate requirement and RS intervals constraints, which is a mixed-integer problem due to the discrete RS interval values. To solve this problem, some numerical methods are typically adopted to obtain the optimal solutions, whose computational complexity grow exponentially with the number of symbols and subcarriers of OFDM. Therefore, we propose a relaxation and approximation method to transform the original discrete problem into a continuous convex one and obtain the sub-optimal solutions. Finally, our proposed scheme is compared with the exhaustive search method in numerical simulations, which show slight gap between the obtained sub-optimal and optimal solutions, and this gap further decreases with large weight factor.