STARS-ISAC: How Many Sensors Do We Need?

A simultaneously transmitting and reflecting surface (STARS) enabled integrated sensing and communications (ISAC) framework is proposed, where a novel bi-directional sensing-STARS architecture is devised to facilitate the full-space communication and sensing. Based on the proposed framework, a joint optimization problem is formulated, where the Cramer-Rao bound (CRB) for estimating the 2-dimension direction-of-arrival of the sensing target is minimized. Two cases are considered for sensing performance enhancement. 1) For the two-user case, an alternating optimization algorithm is proposed. In particular, the maximum number of deployable sensors is obtained in the closed-form expressions. 2) For the multi-user case, an extended CRB (ECRB) metric is proposed to characterize the impact of the number of sensors on the sensing performance. Based on the proposed metric, a novel penalty-based double-loop (PDL) algorithm is proposed to solve the ECRB minimization problem. To tackle the coupling of the ECRB, a general decoupling approach is proposed to convert it to a tractable weighted linear summation form. Simulation results reveal that 1) the proposed PDL algorithm can achieve a near-optimal performance with consideration of sensor deployment; 2) without violating the communication under the quality of service requirements, reducing the receive antennas at the BS does not deteriorate the sensing performance; and 3) it is preferable to deploy more passive elements than sensors in terms of achieving optimal sensing performance