  It is a fundamental problem to analyse the performance bound of
multiple-input multiple-output (MIMO) dual-functional radar-communication
(DFRC) systems. To this end, we derive a performance bound on the communication
function under a constraint on radar performance. To facilitate the analysis,
we consider a toy example, in which there is only one down-link user with a
single receive antenna and one radar target. In such a simplified case, we
obtain an analytical expression for the performance bound and the corresponding
waveform design strategy to achieve the bound. The results reveal a tradeoff
between communication and radar performance, and a condition when the
transmitted energy can be shared between these two functions.
