  In this paper, we propose multi-input multi-output (MIMO) beamforming designs
towards joint radar sensing and multi-user communications. We employ the
Cram\'er-Rao bound (CRB) as a performance metric of target estimation, under
both point and extended target scenarios. We then propose minimizing the CRB of
radar sensing while guaranteeing a pre-defined level of
signal-to-interference-plus-noise ratio (SINR) for each communication user. For
the single-user scenario, we derive a closed form for the optimal solution for
both cases of point and extended targets. For the multi-user scenario, we show
that both problems can be relaxed into semidefinite programming by using the
semidefinite relaxation approach, and prove that the global optimum can always
be obtained. Finally, we demonstrate numerically that the globally optimal
solutions are reachable via the proposed methods, which provide significant
gains in target estimation performance over state-of-the-art benchmarks.
