  Integrated sensing and communication (ISAC) has been envisioned as a solution
to realize the sensing capability required for emerging applications in
wireless networks, while efficiently utilizing the available spectral, hardware
and energy resources. A commonly studied scenario in the ISAC literature
involves a transceiver (e.g., a base station) serving a communication user,
while simultaneously sensing targets from the reflected echo signals, by acting
as a mono-static radar. However, as signal transmission durations are typically
much longer than the radar echo round-trip times, the radar returns are drowned
by the strong self interference (SI) from the transmitter - a phenomenon termed
the echo-miss problem. A promising approach involves the ISAC transceiver to be
full-duplex (FD), and in this paper we jointly design the transmit and receive
beamformers at the transceiver, transmit precoder at the uplink user, and
receive combiner at the downlink user to simultaneously (a) maximize the uplink
and downlink rate, (b) maximize the transmit and receive radar beampattern
power at the target, and (c) suppress the residual SI. Numerical results
illustrate that the proposed design can effectively achieve up to 60 dB
digital-domain SI cancellation, a higher average sum-rate, and more accurate
radar parameter estimation compared with previous ISAC FD studies.
