  We consider the multiple-input multiple-output (MIMO) wiretap channel under a
minimum receiver-side power constraint in addition to the usual maximum
transmitter-side power constraint. This problem is motivated by energy
harvesting communications with wireless energy transfer, where an added goal is
to deliver a minimum amount of energy to a receiver in addition to delivering
secure data to another receiver. In this paper, we characterize the exact
secrecy capacity of the MIMO wiretap channel under transmitter and
receiver-side power constraints. We first show that solving this problem is
equivalent to solving the secrecy capacity of the wiretap channel under a
double-sided correlation matrix constraint on the channel input. We show the
converse by extending the channel enhancement technique to our case. We present
two achievable schemes that achieve the secrecy capacity: the first achievable
scheme uses a Gaussian codebook with a fixed mean, and the second achievable
scheme uses artificial noise (or cooperative jamming) together with a Gaussian
codebook. The role of the mean or the artificial noise is to enable energy
transfer without sacrificing from the secure rate. This is the first instance
of a channel model where either the use of a mean signal or the use of channel
prefixing via artificial noise is strictly necessary for the MIMO wiretap
channel. We then extend our work to consider a maximum receiver-side power
constraint. This problem is motivated by cognitive radio applications, where an
added goal is to decrease the received signal energy (interference temperature)
at a receiver. We further extend our results to: requiring receiver-side power
constraints at both receivers; considering secrecy constraints at both
receivers to study broadcast channels with confidential messages; and removing
the secrecy constraints to study the classical broadcast channel.
