  This paper studies the transmit beamforming in a downlink integrated sensing
and communication (ISAC) system, where a base station (BS) equipped with a
uniform linear array (ULA) sends combined information-bearing and dedicated
radar signals to simultaneously perform downlink multiuser communication and
radar target sensing. Under this setup, we maximize the radar sensing
performance (in terms of minimizing the beampattern matching errors or
maximizing the minimum beampattern gains), subject to the communication users'
minimum signal-to-interference-plus-noise ratio (SINR) requirements and the
BS's transmit power constraints. In particular, we consider two types of
communication receivers, namely Type-I and Type-II receivers, which do not have
and do have the capability of cancelling the interference from the
{\emph{a-priori}} known dedicated radar signals, respectively. Under both
Type-I and Type-II receivers, the beampattern matching and minimum beampattern
gain maximization problems are globally optimally solved via applying the
semidefinite relaxation (SDR) technique together with the rigorous proof of the
tightness of SDR for both Type-I and Type-II receivers under the two design
criteria. It is shown that at the optimality, dedicated radar signals are not
required with Type-I receivers under some specific conditions, while dedicated
radar signals are always needed to enhance the performance with Type-II
receivers. Numerical results show that the minimum beampattern gain
maximization leads to significantly higher beampattern gains at the worst-case
sensing angles with a much lower computational complexity than the beampattern
matching design. It is also shown that by exploiting the capability of
canceling the interference caused by the radar signals, the case with Type-II
receivers results in better sensing performance than that with Type-I receivers
and other conventional designs.
