  This paper investigates the outage probability and the throughput of relay
networks with wireless information and energy transfer where the relays harvest
energy from the transmitted radio-frequency signal of the source. Considering
different power consumption models, we derive the outage probability for both
adaptive and non-adaptive power allocations at the relay. With a total energy
consumption constraint at the source, we provide closed-form expressions for
the optimal time sharing and power allocation between the source energy and
information transfer signals as well as the optimal relay positioning such that
the outage probability is minimized. Finally, we extend our analysis to
multi-relay networks. We show that with perfect channel state information (CSI)
available at the relays and $N$ relays the opportunistic relaying scheme
achieves diversity order of $\frac{N+1}{2}$. Also, we analyze the opportunistic
relaying with partial CSI where either the source-relay or the
relay-destination CSI is provided at its corresponding transmit terminal, and
prove that the relay selection based on the source-relay CSI outperforms the
relay selection based on the relay-destination CSI, in terms of outage
probability. The analytical and simulation results demonstrate the efficiency
of wireless energy and information transfer systems in different conditions.
