  This paper aims to explore the feasibility of the spectrum sharing between
the communication and radar system. We investigate the full-duplex (FD) joint
radar and communication multi-antenna system in which a node labeled ComRad
with a dual communication and radar capability is communicating with a downlink
and an uplink users, as well as detecting the target of interest
simultaneously. Considering a full interference scenario and imperfect channel
state information (CSI), the fundamental performance limits of the FD JRC
system are analyzed. In particular, we first obtain the downlink rate when the
radar signals act as interference. Then, viewing the uplink channel and radar
return channel as a multiple access channel, we propose an alternative
successive interference cancellation scheme, based on which the achievable
uplink communication rate is obtained. For the radar operation, we first derive
the general expression of the estimation rate, which quantifies how much
information is obtained about the target in terms of the direction, the range
and the velocity. Considering the uniform linear antenna array and linear
frequency modulated radar signals, we further obtain the exact closed-form
estimation rate. Numerical simulations reveal that the joint manner of the
communication and radar operations achieves larger rate regions compared to
that of working independently.
