  This paper considers an orthogonal frequency division multiplexing (OFDM)
downlink point-to-point system with simultaneous wireless information and power
transfer. It is assumed that the receiver is able to harvest energy from noise,
interference, and the desired signals.
  We study the design of power allocation algorithms maximizing the energy
efficiency of data transmission (bit/Joule delivered to the receiver). In
particular, the algorithm design is formulated as a high-dimensional non-convex
optimization problem which takes into account the circuit power consumption,
the minimum required data rate, and a constraint on the minimum power delivered
to the receiver. Subsequently, by exploiting the properties of nonlinear
fractional programming, the considered non-convex optimization problem, whose
objective function is in fractional form, is transformed into an equivalent
optimization problem having an objective function in subtractive form, which
enables the derivation of an efficient iterative power allocation algorithm. In
each iteration, the optimal power allocation solution is derived based on dual
decomposition and a one-dimensional search. Simulation results illustrate that
the proposed iterative power allocation algorithm converges to the optimal
solution, and unveil the trade-off between energy efficiency, system capacity,
and wireless power transfer: (1) In the low transmit power regime, maximizing
the system capacity may maximize the energy efficiency. (2) Wireless power
transfer can enhance the energy efficiency, especially in the interference
limited regime.
