  This paper studies a multi-antenna network integrated sensing and
communication (ISAC) system, in which a set of multi-antenna base stations
(BSs) employ the coordinated transmit beamforming to serve their respectively
associated single-antenna communication users (CUs), and at the same time reuse
the reflected information signals to perform joint target detection. In
particular, we consider two target detection scenarios depending on the time
synchronization among BSs. In Scenario \uppercase\expandafter{\romannumeral1},
these BSs are synchronized and can exploit the target-reflected signals over
both the direct links (from each BS to target to itself) and the cross links
(from each BS to target to other BSs) for joint detection. In Scenario
\uppercase\expandafter{\romannumeral2}, these BSs are not synchronized and can
only utilize target-reflected signals over the direct links for joint
detection. For each scenario, we derive the detection probability under a
specific false alarm probability at any given target location. Based on the
derivation, we optimize the coordinated transmit beamforming at the BSs to
maximize the minimum detection probability over a particular target area, while
ensuring the minimum signal-to-interference-plus-noise ratio (SINR) constraints
at the CUs, subject to the maximum transmit power constraints at the BSs. We
use the semi-definite relaxation (SDR) technique to obtain highly-quality
solutions to the formulated problems. Numerical results show that for each
scenario, the proposed design achieves higher detection probability than the
benchmark scheme based on communication design. It is also shown that the time
synchronization among BSs is beneficial in enhancing the detection performance
as more reflected signal paths are exploited.
