  Intelligent reflecting surface (IRS) has shown its effectiveness in
facilitating orthogonal time-division integrated sensing and communications
(TD-ISAC), in which the sensing task and the communication task occupy
orthogonal time-frequency resources, while the role of IRS in the more
interesting scenarios of non-orthogonal ISAC (NO-ISAC) systems has so far
remained unclear. In this paper, we consider an IRS-aided NO-ISAC system, where
a distributed IRS is deployed to assist concurrent communication and location
sensing for a blind-zone user, occupying non-orthogonal/overlapped
time-frequency resources. We first propose a modified Cramer-Rao lower bound
(CRLB) to characterize the performances of both communication and location
sensing in a unified manner. We further derive the closed-form expressions of
the modified CRLB in our considered NO-ISAC system, enabling us to identify the
fundamental trade-off between the communication and location sensing
performances. In addition, by exploiting the modified CRLB, we propose a joint
active and passive beamforming design algorithm that achieves a good
communication and location sensing trade-off. Through numerical results, we
demonstrate the superiority of the IRS-aided NO-ISAC systems over the IRS-aided
TD-ISAC systems, in terms of both communication and localization performances.
Besides, it is shown that the IRS-aided NO-ISAC system with random
communication signals can achieve comparable localization performance to the
IRS-aided localization system with dedicated positioning reference signals.
Moreover, we investigate the trade-off between communication performance and
localization performance and show how the performance of the NO-ISAC system can
be significantly boosted by increasing the number of the IRS elements.
