  In opportunistic cognitive radio networks, when the primary signal is very
weak compared to the background noise, the secondary user requires long sensing
time to achieve a reliable spectrum sensing performance, leading to little
remaining time for the secondary transmission. To tackle this issue, we propose
an active reconfigurable intelligent surface (RIS) assisted spectrum sensing
system, where the received signal strength from the interested primary user can
be enhanced and underlying interference within the background noise can be
mitigated as well. In comparison with the passive RIS, the active RIS can not
only adapt the phase shift of each reflecting element but also amplify the
incident signals. Notably, we study the reflecting coefficient matrix (RCM)
optimization problem to improve the detection probability given a maximum
tolerable false alarm probability and limited sensing time. Then, we show that
the formulated problem can be equivalently transformed to a weighted mean
square error minimization problem using the principle of the well-known
weighted minimum mean square error (WMMSE) algorithm, and an iterative
optimization approach is proposed to obtain the optimal RCM. In addition, to
fairly compare passive RIS and active RIS, we study the required power budget
of the RIS to achieve a target detection probability under a special case where
the direct links are neglected and the RIS-related channels are line-of-sight.
Via extensive simulations, the effectiveness of the WMMSE-based RCM
optimization approach is demonstrated. Furthermore, the results reveal that the
active RIS can outperform the passive RIS when the underlying interference
within the background noise is relatively weak, whereas the passive RIS
performs better in strong interference scenarios because the same power budget
can support a vast number of passive reflecting elements for interference
mitigation.
