STARS-ISAC: How Many Sensors Do We Need?

A simultaneously transmitting and reflecting surface (STARS) enabled two-phase 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 in a time-switching manner. Based on the proposed framework, a joint optimization problem is formulated, where the Cram $\acute {\text {e}}\text{r}$ -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 with the fixed number of sensors, an alternating optimization algorithm is proposed. In particular, the maximum number of deployable sensors is obtained in the closed-form expressions, where the maximum number of sensors is revealed to be only relevant to the QoS requirements of communications. 2) For the multi-user case with the variable number of sensors, an extended CRB (ECRB) metric is proposed to characterize the impact of the number of sensors on the sensing performance. A generic decoupling approach is proposed to convexify the non-convex ECRB expression. Based on this, a novel penalty-based double-loop (PDL) algorithm is proposed. Simulation results reveal that 1) the proposed PDL algorithm achieves a near-optimal performance with consideration of sensor deployment; 2) it is preferable to deploy more passive elements than sensors in terms of achieving optimal sensing performance.