  In this paper, we study simultaneous wireless information and power transfer
(SWIPT) systems employing practical non-linear energy harvester (EH) circuits.
Since the voltage across the reactive elements of realistic EH circuits cannot
drop or rise instantaneously, EHs have memory which we model with a Markov
decision process (MDP). Moreover, since an analytical model that accurately
models all non-linear effects and the unavoidable impedance mismatch of EHs is
not tractable, we propose a learning based model for the EH circuit. We
optimize the input signal distribution for maximization of the harvested power
under a constraint on the minimum mutual information between transmitter (TX)
and information receiver (IR). We distinguish the cases where the MDP state is
known and not known at TX and IR. When the MDP state is known, the formulated
optimization problem for the harvested power is convex. In contrast, if TX and
IR do not know the MDP state, the resulting optimization problem is non-convex
and solved via alternating optimization, which is shown to yield a limit point
of the problem. Our simulation results reveal that the rate-power region of the
considered SWIPT system depends on the symbol duration, the EH input power
level, the EH impedance mismatch, and the type of EH circuit. In particular, a
shorter symbol duration enables higher bit rates at the expense of a
significant decrease in the average harvested power. Furthermore, whereas
half-wave rectifiers outperform full-wave rectifiers in the low and medium
input power regimes, full-wave rectifiers are preferable if the input power at
the EH is high.
