  The wireless domain is witnessing a flourishing of integrated systems, e.g.
(a) integrated sensing and communications, and (b) simultaneous wireless
information and power transfer, due to their potential to use resources
(spectrum, power) judiciously. Inspired by this trend, we investigate
integrated sensing, communications and powering (ISCAP), through the design of
a wideband OFDM signal to power a sensor while simultaneously performing
target-sensing and communication. To characterize the ISCAP performance region,
we assume symbols with non-zero mean asymmetric Gaussian distribution (i.e.,
the input distribution), and optimize its mean and variance at each subcarrier
to maximize the harvested power, subject to constraints on the achievable rate
(communications) and the average side-to-peak-lobe difference (sensing). The
resulting input distribution, through simulations, achieves a larger
performance region than that of (i) a symmetric complex Gaussian input
distribution with identical mean and variance for the real and imaginary parts,
(ii) a zero-mean symmetric complex Gaussian input distribution, and (iii) the
superposed power-splitting communication and sensing signal (the coexisting
solution). In particular, the optimized input distribution balances the three
functions by exhibiting the following features: (a) symbols in subcarriers with
strong communication channels have high variance to satisfy the rate
constraint, while the other symbols are dominated by the mean, forming a
relatively uniform sum of mean and variance across subcarriers for sensing; (b)
with looser communication and sensing constraints, large absolute means appear
on subcarriers with stronger powering channels for higher harvested power. As a
final note, the results highlight the great potential of the co-designed ISCAP
system for further efficiency enhancement.
