  In this work, we consider a multiple-input single-output system in which an
access point (AP) performs a simultaneous wireless information and power
transfer (SWIPT) to serve a user terminal (UT) that is not equipped with
external power supply. In order to assess the efficacy of the SWIPT, we target
a practically relevant scenario characterized by imperfect channel state
information (CSI) at the transmitter, the presence of penalties associated to
the CSI acquisition procedures, and non-zero power consumption for the
operations performed by the UT, such as CSI estimation, uplink signaling and
data decoding. We analyze three different cases for the CSI knowledge at the
AP: no CSI, and imperfect CSI in case of time-division duplexing and
frequency-division duplexing communications. Closed-form representations of the
ergodic downlink rate and both the energy shortage and data outage probability
are derived for the three cases. Additionally, analytic expressions for the
ergodically optimal duration of power transfer and channel estimation/feedback
phases are provided. Our numerical findings verify the correctness of our
derivations, and also show the importance and benefits of CSI knowledge at the
AP in SWIPT systems, albeit imperfect and acquired at the expense of the time
available for the information transfer.
