  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
