  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 target sensing based on the echo signal at the same time. Under
this setup, we aim to reveal the fundamental performance tradeoff limits among
sensing, communication, and powering, in terms of the estimation Cramer-Rao
bound (CRB), achievable communication rate, and harvested energy level,
respectively. In particular, we consider two different target models for radar
sensing, namely the point and extended targets, for which we are interested in
estimating the target angle and the complete target response matrix,
respectively. For both models, 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 well-structured optimal
transmit covariance solutions to the two formulated problems 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 schemes based on time switching and eigenmode transmission (EMT).
