  This article studies and derives beamforming design in a dual-functional
radar-communication (DFRC) multiple-input-multiple-output system. We focus on a
scenario, where the DFRC base station communicates with downlink communication
users, with imperfect channel state information knowledge, and performs target
detection, all via the same transmit signal. Through careful relaxation
procedures, we arrive at a suitable and novel optimization problem, which
maximizes the radar output power in the Bartlett sense, under probabilistic
outage signal-to-interference-and-noise ratio constraints. Theoretical analysis
proves optimality of the solution given by the relaxed version of the problem,
as well as closed-form solutions in certain scenarios. Finally, the achieved
performances and trade-offs of the proposed beamforming design are demonstrated
through numerical simulations.
