  Beamforming design has been widely investigated for integrated sensing and
communication (ISAC) systems with full-duplex (FD) sensing and half-duplex (HD)
communication. To achieve higher spectral efficiency, in this paper, we extend
existing ISAC beamforming design by considering the FD capability for both
radar and communication. Specifically, we consider an ISAC system, where the
base station (BS) performs target detection and communicates with multiple
downlink users and uplink users reusing the same time and frequency resources.
We jointly optimize the downlink dual-functional transmit signal and the uplink
receive beamformers at the BS and the transmit power at the uplink users. The
problem is formulated to minimize the total transmit power of the system while
guaranteeing the communication and sensing requirements. The downlink and
uplink transmissions are tightly coupled, making the joint optimization
challenging. To handle this issue, we first determine the receive beamformers
in closed forms with respect to the BS transmit beamforming and the user
transmit power and then suggest an iterative solution to the remaining problem.
We demonstrate via numerical results that the optimized FD communication-based
ISAC leads to power efficiency improvement compared to conventional ISAC with
HD communication.
