  This paper unifies integrated sensing and communication (ISAC) and
simultaneous wireless information and power transfer (SWIPT), by investigating
a new multi-functional multiple-input multiple-output (MIMO) system integrating
wireless sensing, communication, and powering. In this system, one
multi-antenna hybrid access point (H-AP) transmits wireless signals to
communicate with one multi-antenna information decoding (ID) receiver,
wirelessly charge one multi-antenna energy harvesting (EH) receiver, and
perform radar sensing for a point target based on the echo signal at the same
time. Under this setup, we aim to reveal the fundamental performance tradeoff
limits of sensing, communication, and powering, in terms of the estimation
Cram{\'e}r-Rao bound (CRB), achievable communication rate, and harvested energy
level, respectively. Towards this end, we define the achievable CRB-rate-energy
(C-R-E) region and characterize its Pareto boundary by maximizing the
achievable rate at the ID receiver, subject to the estimation CRB requirement
for target sensing, the harvested energy requirement at the EH receiver, and
the maximum transmit power constraint at the H-AP. We obtain the
semi-closed-form optimal transmit covariance solution to the formulated problem
by applying advanced convex optimization techniques. Numerical results show the
optimal C-R-E region boundary achieved by our proposed design, as compared to
the benchmark scheme based on time switching.
