  A simultaneously transmitting and reflecting intelligent surface (STARS)
enabled integrated sensing and communications (ISAC) framework is proposed,
where the whole space is divided by STARS into a sensing space and a
communication space. A novel sensing-at-STARS structure, where dedicated
sensors are installed at the STARS, is proposed to address the significant path
loss and clutter interference for sensing. The Cramer-Rao bound (CRB) of the
2-dimension (2D) direction-of-arrivals (DOAs) estimation of the sensing target
is derived, which is then minimized subject to the minimum communication
requirement. A novel approach is proposed to transform the complicated CRB
minimization problem into a trackable modified Fisher information matrix (FIM)
optimization problem. Both independent and coupled phase-shift models of STARS
are investigated: 1) For the independent phase-shift model, to address the
coupling of ISAC waveform and STARS coefficient in the modified FIM, an
efficient double-loop iterative algorithm based on the penalty dual
decomposition (PDD) framework is conceived; 2) For the coupled phase-shift
model, based on the PDD framework, a low complexity alternating optimization
algorithm is proposed to tackle coupled phase-shift constants by alternatively
optimizing amplitude and phase-shift coefficients in closed-form. Finally, the
numerical results demonstrate that: 1) STARS significantly outperforms the
conventional RIS in CRB under the communication constraints; 2) The coupled
phase-shift model achieves comparable performance to the independent one for
low communication requirements or sufficient STARS elements; 3) It is more
efficient to increase the number of passive elements of STARS rather than the
active elements of the sensor; 4) High sensing accuracy can be achieved by
STARS using the practical 2D maximum likelihood estimator compared with the
conventional RIS.
